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Popular >

simplify log_{0.1}(10)

Solution

simplify

lo g_{0.1} (10)

Solution

- 1

Solution steps

lo g_{0.1} (10)

Convert

0.1

to a fraction:

\frac{1}{10}

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

Apply log rule:

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

= - lo g_{10} (10)

Rewrite

10

in power-base form:

10 = 1 0^{1}

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

Apply log rule:

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

lo g_{10} (1 0^{1}) = 1 \cdot lo g_{10} (10)

= - 1 \cdot lo g_{10} (10)

Apply log rule:

lo g_{a} (a) = 1

lo g_{10} (10) = 1

= - 1 \cdot 1

Multiply the numbers:

- 1 \cdot 1 = - 1

= - 1

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Frequently Asked Questions (FAQ)

What is log_{0.1}(10) ?
The solution to log_{0.1}(10) is -1