Find the exact solution of the exponential equation in terms

tugmiddelc0

tugmiddelc0

Answered question

2021-11-21

Find the exact solution of the exponential equation in terms of logarithms.
Use a calculator to find an approximation to the solution rounded to six decimal places.
I keep getting a negative log answer and decimal...i dont

Answer & Explanation

Feas1981

Feas1981

Beginner2021-11-22Added 16 answers

Our aim is to find the exact the exact solution of the exponential equation
81x=9(i) in terms of logarithms.
Taking the logarithmic of equation−(i) both sides we have:−
ln(81x)=ln(9)(ii)
Now, using Logarithmic Power Rule in L.H.S of equation (ii), we have:−
logb(xy)=ylogb(x)[Logarithmic Power Rule]
(1x)ln(8)=ln(9)(iii)
Applying Distributive Property in L.H.S. of equation (iii), we have:−
ln(8)xln(8)=ln(9)
xln(8)=ln(9)ln(8)
x=ln(9)ln(8)ln(9)
x=2.1972242.0794412.079441
x=0.1177832.079441
x=0.056642  is the exact solution of exponential equation  81x=9  upto 6 decimal places.
Ourst1977

Ourst1977

Beginner2021-11-23Added 21 answers

Thank you very much for the solution, I have been looking for it for a long time and could not find

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