How do you solve #81=(\frac{1}{3})^{5x-6}#?

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Answer 1 · 2017-10-29T21:41:45

# x = 2/5#

We can solve this by taking logorithms from both sides, but we can consider how #3^4 = 81#

So hence becoming;

#3^4 = (1/3)^(5x-6)#

Then further note how #(1/3)^-4 = 81#

So hence becoming #(1/3)^-4 = (1/3)^(5x-6)#

Note how the bases are now the same, so hence #-4 = 5x-6#

So solving to yield; # x = 2/5#