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3^x=9x ,find x

3^x=9x ,find x



To solve this equation, we can take the natural logarithm of both sides:
ln(3^x) = ln(9x)
Using the property of logarithms that ln(a^b) = b ln(a), we can simplify the left-hand side:
x ln(3) = ln(9x)
Next, we isolate x on one side by dividing both sides by ln(3):
x = ln(9x) / ln(3)
We can use a numerical method such as Newton's method to approximate the value of x. Let's start with an initial guess of x=1:
x1 = ln(9*1) / ln(3) ≈ 1.617
Next, we can use this value to compute a new estimate:
x2 = ln(9*x1) / ln(3) ≈ 1.881
We can repeat this process with increasing accuracy until the estimate converges to a certain value:
x3 ≈ 1.945 x4 ≈ 1.959 x5 ≈ 1.962 x6 ≈ 1.963
So the solution to the equation 3^x = 9x is approximately x ≈ 1.963.Kwa hisani ya chatgpt mimi hesabu sizijui.
 
Wadau naomba jibu,

the following consecutive readings were taken with a level and a 4m levelling staff on a continuously sloping ground at common interval of 30m.0.855 on A,1.545,2.335,3.115,3.825,0.455,1.380,2.055,2.855,3.455,0.585,1.015,1.850,2.755 and 3.845 on B(a)make the entries in a level book and apply the usual check (b) determine the gradient of AB
 
Wadau naomba jibu,

the following consecutive readings were taken with a level and a 4m levelling staff on a continuously sloping ground at common interval of 30m.0.855 on A,1.545,2.335,3.115,3.825,0.455,1.380,2.055,2.855,3.455,0.585,1.015,1.850,2.755 and 3.845 on B(a)make the entries in a level book and apply the usual check (b) determine the gradient of A

the following consecutive readings were taken with a level and a 4m levelling staff on a continuously sloping ground at common interval of 30m.0.855 on A,1.545,2.335,3.115,3.825,0.455,1.380,2.055,2.855,3.455,0.585,1.015,1.850,2.755 and 3.845 on B(a)make the entries in a level book and apply the usual check (b) determine the gradient of AB



a) Entries in the level book:
StationBacksight (BS)Foresight (FS)Height of Instrument (HI)Reduced Level (RL)
A-0.855100.855-
B10.8551.545101.40099.545
B21.5452.335100.94598.755
B32.3353.115100.59098.070
B43.1153.825100.23597.370
C13.8250.455100.680100.235
C20.4551.380101.13598.975
C31.3802.055100.68098.300
C42.0552.855100.22597.510
C52.8553.45599.77096.650
D13.4550.585100.21599.770
D20.5851.015100.77098.385
D31.0151.850100.31597.450
D41.8502.75599.86096.535
D52.7553.84599.40595.510
b) To determine the gradient of AB, we need to calculate the rise and run between A and B.
The height of instrument (HI) at A is 100.855 m. The reduced level (RL) at B1 is 99.545 m. Therefore, the rise between A and B1 is:
rise = HI - RL = 100.855 - 99.545 = 1.31 m
The horizontal distance between A and B1 is 30 m. Therefore, the run between A and B1 is:
run = 30 m
We can calculate the gradient between A and B as:
gradient = rise / run = 1.31 / 30 = 0.0437
Therefore, the gradient of AB is 0.0437 or 1 in 22.9. Kwa hisani ya chatgpt
 

3^x=9x ,find x



To solve this equation, we can take the natural logarithm of both sides:
ln(3^x) = ln(9x)
Using the property of logarithms that ln(a^b) = b ln(a), we can simplify the left-hand side:
x ln(3) = ln(9x)
Next, we isolate x on one side by dividing both sides by ln(3):
x = ln(9x) / ln(3)
We can use a numerical method such as Newton's method to approximate the value of x. Let's start with an initial guess of x=1:
x1 = ln(9*1) / ln(3) ≈ 1.617
Next, we can use this value to compute a new estimate:
x2 = ln(9*x1) / ln(3) ≈ 1.881
We can repeat this process with increasing accuracy until the estimate converges to a certain value:
x3 ≈ 1.945 x4 ≈ 1.959 x5 ≈ 1.962 x6 ≈ 1.963
So the solution to the equation 3^x = 9x is approximately x ≈ 1.963.Kwa hisani ya chatgpt mimi hesabu sizijui.
Jibu ni x=3 na si 1.963 asante kwa kujaribu pia mkuu ,
 
the following consecutive readings were taken with a level and a 4m levelling staff on a continuously sloping ground at common interval of 30m.0.855 on A,1.545,2.335,3.115,3.825,0.455,1.380,2.055,2.855,3.455,0.585,1.015,1.850,2.755 and 3.845 on B(a)make the entries in a level book and apply the usual check (b) determine the gradient of AB



a) Entries in the level book:
StationBacksight (BS)Foresight (FS)Height of Instrument (HI)Reduced Level (RL)
A-0.855100.855-
B10.8551.545101.40099.545
B21.5452.335100.94598.755
B32.3353.115100.59098.070
B43.1153.825100.23597.370
C13.8250.455100.680100.235
C20.4551.380101.13598.975
C31.3802.055100.68098.300
C42.0552.855100.22597.510
C52.8553.45599.77096.650
D13.4550.585100.21599.770
D20.5851.015100.77098.385
D31.0151.850100.31597.450
D41.8502.75599.86096.535
D52.7553.84599.40595.510
b) To determine the gradient of AB, we need to calculate the rise and run between A and B.
The height of instrument (HI) at A is 100.855 m. The reduced level (RL) at B1 is 99.545 m. Therefore, the rise between A and B1 is:
rise = HI - RL = 100.855 - 99.545 = 1.31 m
The horizontal distance between A and B1 is 30 m. Therefore, the run between A and B1 is:
run = 30 m
We can calculate the gradient between A and B as:
gradient = rise / run = 1.31 / 30 = 0.0437
Therefore, the gradient of AB is 0.0437 or 1 in 22.9. Kwa hisani ya chatgpt
Shukrani sana kiongozi .pia Nifundisheni namna ya kuitumia,nmewah ingia lakini hata haifunguki.msaada tafazali

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3^x=9x ,find x



To solve this equation, we can take the natural logarithm of both sides:
ln(3^x) = ln(9x)
Using the property of logarithms that ln(a^b) = b ln(a), we can simplify the left-hand side:
x ln(3) = ln(9x)
Next, we isolate x on one side by dividing both sides by ln(3):
x = ln(9x) / ln(3)
We can use a numerical method such as Newton's method to approximate the value of x. Let's start with an initial guess of x=1:
x1 = ln(9*1) / ln(3) ≈ 1.617
Next, we can use this value to compute a new estimate:
x2 = ln(9*x1) / ln(3) ≈ 1.881
We can repeat this process with increasing accuracy until the estimate converges to a certain value:
x3 ≈ 1.945 x4 ≈ 1.959 x5 ≈ 1.962 x6 ≈ 1.963
So the solution to the equation 3^x = 9x is approximately x ≈ 1.963.Kwa hisani ya chatgpt mimi hesabu sizijui.
If 3^x=9x
Divìde by 9 throughout the eqn
3^x/9=x
Expressing 9 in terms of base 3
3^x/3^2=x
3^(x-2)=x^1
Compare either the base au exponents
(x-2)=1 or 3=x
x-2=1
x=3
Therefore,x=3

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