How do you solve this using logarithms?

Question

Use logarithms to find $x$ $x$

$3 {(x)}^{0.6223} = 1.266$ $3(x)^0.6223=1.266$

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Answer 1 · 2018-04-20T07:53:13

$x = e^{\frac{ln (0.422)}{0.6223}} \approx 0.2499763052$ $color(blue)(x=e^((ln(0.422))/0.6223)~~0.2499763052)$

$3 x^{0.6223} = 1.266$ $3x^(0.6223)=1.266$

Divide by 3:

$x^{0.6223} = 0.422$ $x^(0.6223)=0.422$

Taking natural logarithms of both sides:

$0.6223 ln (x) = ln (0.422)$ $0.6223ln(x)=ln(0.422)$

Divide by $0.6223$ $0.6223$ :

$ln (x) = \frac{ln (0.422)}{0.6223}$ $ln(x)=(ln(0.422))/0.6223$

Raising $e$ $bbe$ to the power of each side:

$e^{ln (x)} = e^{\frac{ln (0.422)}{0.6223}}$ $e^(ln(x))=e^((ln(0.422))/0.6223)$

$x = e^{\frac{ln (0.422)}{0.6223}} \approx 0.2499763052$ $x=e^((ln(0.422))/0.6223)~~0.2499763052$