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

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Answer 1 · 2016-10-30T03:14:54

$x = 20$ $x=20$

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

Add $4$ $4$ to both sides.

$3^{0.1 x} = 9$ $3^(0.1x)=9$

Take the log of both sides.

${log 3}^{0.1 x} = log 9$ $log 3^(0.1x)= log9$

Use the log rule ${log x}^{a} = a log x$ $logx^a=alogx$

$0.1 x log 3 = log 9$ $0.1x log3=log9$

Divide both sides by $0.1 log 3$ $0.1 log3$

$x = \frac{log 9}{0.1 log 3} = \frac{10 log 9}{log 3}$ $x=log9/(0.1 log3)=(10log9)/log3$

Use the change of base formula ${log}_{b} a = \frac{log a}{log b}$ $log_ba=loga/logb$

$x = 10 \cdot {log}_{3} 9$ $x=10 * log_3 9$

${log}_{3} 9 = 2$ $log_3 9 = color(red)2$ because $3^{2} = 9$ $3^color(red)2=9$

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

How do you solve 30.1x−4=53^(0.1x)-4=5?