What is simplify-log_{10}(625*10^{-3}) ?

The solution to simplify-log_{10}(625*10^{-3}) is -4log_{10}(5)+3

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simplify-log_{10}(625*10^{-3})

simplify

- lo g_{10} (625 \cdot 1 0^{- 3})

- 4 lo g_{10} (5) + 3

Decimal Notation

0.20411 \dots

Solution steps

- lo g_{10} (625 \cdot 1 0^{- 3})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (625 \cdot 1 0^{- 3}) = lo g_{10} (625) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (625) + lo g_{10} (1 0^{- 3}))

Apply log rule:

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

lo g_{10} (1 0^{- 3}) = - 3 lo g_{10} (10)

= - (lo g_{10} (625) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (625) - 3)

lo g_{10} (625) = 4 lo g_{10} (5)

= - (4 lo g_{10} (5) - 3)

Distribute parentheses

= - (4 lo g_{10} (5)) - (- 3)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - 4 lo g_{10} (5) + 3

- \frac{6}{5} ln (2) - \frac{1}{5} ln (3)

ln (\frac{25}{80})

\frac{25.5 \cdot 38}{292 \cdot 1 0 ^{- 3} \cdot 8} ln (\frac{780}{450})

\frac{1}{2} ln (43 + 8) - \frac{1}{2} ln (4)

\frac{7 ln ( 101 )}{2} + 534

What is simplify-log_{10}(625*10^{-3}) ?
The solution to simplify-log_{10}(625*10^{-3}) is -4log_{10}(5)+3