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Algebra Level 2

3 log ⁡ 2 + log ⁡ ( 45 − 4 x ) = 2 + log ⁡ ( x − 3 ) 3 \log 2 + \log (45-4x) = 2 + \log (x-3)
x = ? x = ?


The answer is 5.

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Noel Lo by Noel Lo , 24, Singapore

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1 solution

Noel Lo
Mar 27, 2015

3 l g 2 + l g ( 45 − 4 x ) = 2 + l g ( x − 3 ) 3 lg 2 + lg (45 - 4x) = 2+ lg (x-3)

l g 2 3 + l g ( 45 − 4 x ) = l g 1 0 2 + l g ( x − 3 ) lg 2^3 + lg (45-4x) = lg 10^2 + lg (x-3)

l g 8 ( 45 − 4 x ) = l g 100 ( x − 3 ) lg 8(45-4x) = lg 100(x-3)

360 − 32 x = 100 x − 300 360-32x = 100x - 300

132 x = 660 132x=660

x = 660 132 x=\frac{660}{132} = 5 \boxed{5}

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