How do you solve $log_9(x^7)=15$ ?

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Answer 1 · 2015-12-16T23:49:50

$x = 9^(15/7)$

From the definition of a logarithm, we have

$a^(log_a(x)) = x$

Applying that here, we get

$log_9(x^7) = 15$

$=> 9^(log_9(x^7)) = 9^15$

$=> x^7 = 9^15$

$=> x = (9^15)^(1/7) = 9^(15/7)$

Answer 2 · 2015-12-17T04:05:04

$x=9^(15/7)$

Use the logarithm rule: $log_a(b^c)=c*log_a(b)$

Thus, the equation can be rewritten as

$7log_9(x)=15$

Divide both sides by $7$

$log_9(x)=15/7$

Undo the logarithm

$9^(log_9(x)=9^(15/7)$

$x=9^(15/7)$

How do you solve log_9(x^7)=15 log_9(x^7)=15 ?