How do you solve $2*7^(6x) -8 =16$ and find any extraneous solutions?

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Answer 1 · 2016-08-20T18:52:26

$:. x=1.277/6=0.2128$

$2*7^(6x)-8=16$

$:. 2*7^(6x)=16+8=24$

$:. 7^(6x)=24/2=12$

$:. 6x=log_7 12$

By the Change of Base Rule, we have,

$6x=log_10 12/log_10 7=1.0792/0.8451=1.277$

$:. x=1.277/6=0.2128$

How do you solve 2*7^(6x) -8 =162*7^(6x) -8 =16 and find any extraneous solutions?