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How to solve 2^x-6 = 7^2x

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Solve the following equation for x

2^x-6 = 7^2x

It's said that I should use base -10 logarithms.
asked Aug 18, 2017 in Algebra by Karen

1 Answer

2x-6 = 72x

log 2x-6 = log 72x

(x - 6)(log 2) = 2x(log 7)

(x)(log 2) - 6(log 2) = 2x(log 7)

-6(log 2) = 2x(log 7) - xlog 2

-6(log2) = x[2log 7 - log 2]

(-6 log 2) / (2log 7 - log 2] = x

answered Aug 21, 2017 by quickwriter (2,510 points)
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