How do you solve $3 log_5 x - log_5 4 = log_5 16$ ?

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Answer 1 · 2015-06-18T21:39:13

The answer is $x=4$

To solve this equation you have to use the facts that:

First you use (1) to get:

$log_5(x^3) -log_5(4)=log_5(16)$

Then you use (2) to get:

$log_5(x^3/4) =log_5(16)$

Now you can leave the logarithms (they both have the same base)

$x^3/4=16$

$x^3=64$

$x=4$ (because $4^3=4*4*4=64$ )

How do you solve 3 log_5 x - log_5 4 = log_5 163 log_5 x - log_5 4 = log_5 16?