What is simplify-log_{10}(1.66*10^{(-5)}) ?

The solution to simplify-log_{10}(1.66*10^{(-5)}) is -log_{10}(1.66)+5

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simplify-log_{10}(1.66*10^{(-5)})

simplify

- lo g_{10} (1.66 \cdot 1 0^{(- 5)})

- lo g_{10} (1.66) + 5

Decimal Notation

4.77989 \dots

Solution steps

- lo g_{10} (1.66 \cdot 1 0^{(- 5)})

Apply log rule:

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

lo g_{10} (1.66 \cdot 1 0^{(- 5)}) = lo g_{10} (1.66) + lo g_{10} (1 0^{(- 5)})

= - (lo g_{10} (1.66) + lo g_{10} (1 0^{(- 5)}))

Apply log rule:

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

lo g_{10} (1 0^{(- 5)}) = (- 5) lo g_{10} (10)

= - (lo g_{10} (1.66) + (- 5) lo g_{10} (10))

Remove parentheses:

(- a) = - a

= - (lo g_{10} (1.66) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (1.66) - 5)

Distribute parentheses

= - (lo g_{10} (1.66)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (1.66) + 5

\frac{1}{2} (ln (8) - ln (3))

lo g_{π} (\frac{22}{7})

ln (\frac{2000}{0.0012 \cdot ( - 5 \cdot 1 0 ^{16} )})

\frac{1}{10} ln (\frac{70}{80})

\frac{- ln ( \frac{y}{x} ) - 1}{x} + \frac{1}{x} + ln (\frac{y}{x})

What is simplify-log_{10}(1.66*10^{(-5)}) ?
The solution to simplify-log_{10}(1.66*10^{(-5)}) is -log_{10}(1.66)+5