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Popular >

simplify log_{0.01}(10)

Solution

simplify

lo g_{0.01} (10)

Solution

- 0.5

Solution steps

lo g_{0.01} (10)

Convert

0.01

to a fraction:

\frac{1}{100}

= lo g_{\frac{1}{100}} (10)

Apply log rule:

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

= - lo g_{100} (10)

Rewrite

100

as

1 0^{2}

= - lo g_{1 0^{2}} (10)

Apply log rule:

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

lo g_{1 0^{2}} (10) = \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_{0.01}(10) ?
The solution to log_{0.01}(10) is -0.5