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Popular >

simplify-log_{10}(0.04)

Solution

simplify

- lo g_{10} (0.04)

Solution

2 lo g_{10} (5)

+1

Decimal Notation

1.39794 \dots

Solution steps

- lo g_{10} (0.04)

0.04 = \frac{4}{100}

= - lo g_{10} (\frac{4}{100})

Cancel the numbers:

\frac{4}{100} = \frac{1}{25}

= - lo g_{10} (\frac{1}{25})

\frac{1}{25} = 2 5^{- 1}

= - lo g_{10} (2 5^{- 1})

Apply log rule:

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

lo g_{10} (2 5^{- 1}) = - 1 \cdot lo g_{10} (25)

= - (- 1 \cdot lo g_{10} (25))

Apply rule:

1 \cdot a = a

- 1 \cdot lo g_{10} (25) = - lo g_{10} (25)

= - (- lo g_{10} (25))

Factor the number:

25 = 5^{2}

= - (- lo g_{10} (5^{2}))

Apply log rule:

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

- lo g_{10} (5^{2}) = - 2 lo g_{10} (5)

= - (- 2 lo g_{10} (5))

Apply rule:

- (- a) = a

- (- 2 lo g_{10} (5)) = 2 lo g_{10} (5)

= 2 lo g_{10} (5)

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Frequently Asked Questions (FAQ)

What is simplify-log_{10}(0.04) ?
The solution to simplify-log_{10}(0.04) is 2log_{10}(5)