(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find x in the following equation

(ln 64 / 2) + ln x = ln 18 - ln x

The answer should be x = 3/2

2. Relevant equations

Logarithm laws

ln m - ln n = ln (m/n)

3. The attempt at a solution

I tried two methods:

(ln 64 / 2) + ln x = ln 18 - ln x

ln 32 + ln x = ln 18 - ln x

ln 32 - ln 18 = - ln x - ln x

ln (32/18) = -2 ln x

ln (32/18) = ln x^{-2}

(32/18) = x^{-2}

(32/18)^{1/-2}= x

0.75 = 3/4 = x

Wrong answer

(ln 64 / 2) + ln x = ln 18 - ln x

ln 64 + ln x = 2 (ln 18 - ln x)

ln 64 + ln x = 2 ln 18 - 2 ln x

ln 64 + ln x = ln 18^{2}- ln x^{2}

ln 64 - ln 18^{2}= - ln x - ln x^{2}

ln 64 - ln 324 = - ln x - 2 ln x

ln 64 - ln 324 = - 3 ln x

ln 64 - ln 324 = ln x^{-3}

ln (64/324) = ln x^{-3}

(64/324) = x^{-3}

(64/324)^{1/-3}= x

1.717 = x

Wrong answer again.

The first steps seem to be more right to me though but I can't find what I did incorrect..

Thank you in advanced.

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# Homework Help: Logarithm Equation Problem

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