How do you solve $\log _ { 9} ( 2x + 5) = \log _ { 9} 5x$ ?

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Answer 1 · 2017-03-02T19:04:32

$x=5/3$

Because you have a $log_9$ on both sides, raise both sides as powers of $9$ , which effectively cancels out the $log$ s.

$log_9(2x+5) = log_9(5x)$

$9^(log_9(2x+5)) = 9^(log_9(5x))$

$2x+5 = 5x$

Now you can simply solve

$2x+5=5x$

$5=3x$

$x=5/3$

How do you solve \log _ { 9} ( 2x + 5) = \log _ { 9} 5x\log _ { 9} ( 2x + 5) = \log _ { 9} 5x?