What is simplify-log_{10}(1.65*10^{-5}) ?

The solution to simplify-log_{10}(1.65*10^{-5}) is -log_{10}(1.65)+5

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simplify-log_{10}(1.65*10^{-5})

simplify

- lo g_{10} (1.65 \cdot 1 0^{- 5})

- lo g_{10} (1.65) + 5

Decimal Notation

4.78251 \dots

Solution steps

- lo g_{10} (1.65 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (1.65 \cdot 1 0^{- 5}) = lo g_{10} (1.65) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (1.65) + 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} (1.65) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (1.65) - 5)

Distribute parentheses

= - (lo g_{10} (1.65)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (1.65) + 5

ln (\frac{x ^{2} - y ^{2}}{x ^{2} + y ^{2}})

(\frac{1}{( 1.21 \cdot 1 0 ^{(- 4)} )}) \cdot ln (\frac{15.3}{5.22})

0.199 ln (\frac{0.105}{0.075})

ln (\frac{x - 1}{x + 1}) - \frac{2 x}{( x ^{2} - 1 )}

\frac{1}{20} ln (\frac{33}{28})

What is simplify-log_{10}(1.65*10^{-5}) ?
The solution to simplify-log_{10}(1.65*10^{-5}) is -log_{10}(1.65)+5