How do you solve $3^(0.1x)-4=5$ ?

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Answer 1 · 2016-10-30T03:14:54

$x=20$

$3^(0.1x) -4=5$

Add $4$ to both sides.

$3^(0.1x)=9$

Take the log of both sides.

$log 3^(0.1x)= log9$

Use the log rule $logx^a=alogx$

$0.1x log3=log9$

Divide both sides by $0.1 log3$

$x=log9/(0.1 log3)=(10log9)/log3$

Use the change of base formula $log_ba=loga/logb$

$x=10 * log_3 9$

$log_3 9 = color(red)2$ because $3^color(red)2=9$

$x=10*color(red)2= 20$

How do you solve 3^(0.1x)-4=53^(0.1x)-4=5?