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Popular >

simplify log_{0.04}(5)

Solution

simplify

lo g_{0.04} (5)

Solution

- 0.5

Solution steps

lo g_{0.04} (5)

Convert

0.04

to a fraction:

\frac{1}{25}

= lo g_{\frac{1}{25}} (5)

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

= - lo g_{25} (5)

Rewrite

25

as

5^{2}

= - lo g_{5^{2}} (5)

Apply log rule:

lo g_{x^{n}} (x) = \frac{1}{n}

lo g_{5^{2}} (5) = \frac{1}{2}

= - \frac{1}{2}

Convert element to a decimal form

\frac{1}{2} = 0.5

= - 0.5

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Frequently Asked Questions (FAQ)

What is log_{0.04}(5) ?
The solution to log_{0.04}(5) is -0.5