Solving an exponential equation Alright, here's the equation: \(\displaystyle‎{1.08}^{{x}}={1.10}^{{{x}-{1}}}\) I

markush35q

markush35q

Answered question

2022-04-03

Solving an exponential equation
Alright, here's the equation:
1.08x=1.10x1
I know I need to use logarithms, but I can't figure how to do it. Thanks in advance!

Answer & Explanation

Theodore Davila

Theodore Davila

Beginner2022-04-04Added 14 answers

Don't get hung up on the fact that the bases don't match. The so-called power rule (or exponent rule) for logarithms works for any base.
1.08x=1.10x1
ln(1.08x)=ln(1.10x1)
xln(1.08)=(x1)ln(1.10)
xln(1.08)=xln(1.10)ln(1.10)
xln(1.08)xln(1.10)=ln(1.10)
x(ln(1.08)ln(1.10))=ln(1.10)
x=ln(1.10)ln(1.08)ln(1.10)

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