What is log_{2/5}((625/16)^2) ?

The solution to log_{2/5}((625/16)^2) is 8log_{2/5}(5)-8log_{2/5}(2)

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simplify log_{2/5}((625/16)^2)

simplify

lo g_{\frac{2}{5}} ((\frac{625}{16})^{2})

8 lo g_{\frac{2}{5}} (5) - 8 lo g_{\frac{2}{5}} (2)

Decimal Notation

- 8

Solution steps

lo g_{\frac{2}{5}} ((\frac{625}{16})^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{\frac{2}{5}} ((\frac{625}{16})^{2}) = 2 lo g_{\frac{2}{5}} (\frac{625}{16})

= 2 lo g_{\frac{2}{5}} (\frac{625}{16})

lo g_{\frac{2}{5}} (\frac{625}{16}) = 4 lo g_{\frac{2}{5}} (5) - 4 lo g_{\frac{2}{5}} (2)

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

Expand

2 (4 lo g_{\frac{2}{5}} (5) - 4 lo g_{\frac{2}{5}} (2)) : 8 lo g_{\frac{2}{5}} (5) - 8 lo g_{\frac{2}{5}} (2)

= 8 lo g_{\frac{2}{5}} (5) - 8 lo g_{\frac{2}{5}} (2)

(4^{x})^{2}

(x - 1) (x + 2) (x + 1)

x^{3} y^{6} - 64

\frac{( 2 x ) ^{- 4}}{x ^{- 1} \cdot x}

\frac{x ^{15} + y ^{15}}{x ^{3} + y ^{3}}

What is log_{2/5}((625/16)^2) ?
The solution to log_{2/5}((625/16)^2) is 8log_{2/5}(5)-8log_{2/5}(2)