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

Resolve the following equation:

log_{2}x + log_{2}[(x-3)/5)] = 3

2. Relevant equations

Logarithmic laws:

log_{c}m + log_{c}n = log_{c}mn

3. The attempt at a solution

Restriction:

(x-3)/5 > 0

x-3 > 0

x > 3

Resolution:

log_{2}x + log_{2}[(x-3)/5)] = 3

log_{2}x[(x-3)/5)] = 3

log_{2}[(x^{2}- 3x)/5x] = 3

2^{3}= (x^{2}- 3x)/5x

8 = (x^{2}- 3x)/5x

8(5x) = x^{2}- 3x

40x = x^{2}- 3x

40x + 3x = x^{2}

43x = x^{2}

43 = x^{2}/ x

43 = x

My answer book says the answer is 8 however I don't seem to get to that after numerous attempts.

Thank you in advanced.

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# Homework Help: Resolution of a logarithmic function

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