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How do you solve ${log}_{b} (3) = .234$ $log_b(3) = .234$ ?

1 Answer

Apr 18, 2016

$b \approx 109.39$ $b~~109.39$

Explanation:

If ${log}_{b} (3) = .234$ $log_b (3) = .234$
then (by definition of $log$ $log$
$XXX b^{.234} = 3$ $color(white)("XXX")b^.234 = 3$

$XXX {(b^{.234})}^{\frac{1}{.234}} = 3^{\frac{1}{.234}}$ $color(white)("XXX")(b^.234)^(1/.234)=3^(1/.234)$

$XXX b = 3^{\frac{1}{.234}} \approx 3^{4.2735} \approx 109.3905$ $color(white)("XXX")b=3^(1/.234)~~3^4.2735~~109.3905$

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