What is changebase log_{4}(32) ?

The solution to changebase log_{4}(32) is 5/2

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changebase log_{4}(32)

change base

lo g_{4} (32)

\frac{5}{2}

Decimal

2.5

Solution steps

lo g_{4} (32)

Apply log rule:

lo g_{a} (b) = \frac{lo g _{c} ( b )}{lo g _{c} ( a )}

lo g_{4} (32) = \frac{ln ( 32 )}{ln ( 4 )}

= \frac{ln ( 32 )}{ln ( 4 )}

Simplify

ln (4) : 2 ln (2)

= \frac{ln ( 32 )}{2 ln ( 2 )}

Simplify

ln (32) : 5 ln (2)

= \frac{5 ln ( 2 )}{2 ln ( 2 )}

Cancel the common factor:

ln (2)

= \frac{5}{2}

\frac{1}{2} ln (\frac{11}{5})

ln (- 6 \frac{e ^{(x)}}{3})

ln (1^{2} (1 + 2)^{\frac{9}{5}} (1 - 3)^{\frac{1}{5}})

3 ln (4) - \frac{1}{2} ln (x^{2} + 3)

\frac{3}{5} lo g_{\frac{4}{25}} (5) - \frac{3}{5} lo g_{\frac{4}{25}} (2)