What is simplify-log_{10}(2.29x)10^{-7} ?

The solution to simplify-log_{10}(2.29x)10^{-7} is 1/5000000-(log_{10}(229)+log_{10}(x))/(10000000)

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simplify-log_{10}(2.29x)10^{-7}

simplify

- lo g_{10} (2.29 x) 1 0^{- 7}

\frac{1}{5000000} - \frac{lo g _{10} ( 229 ) + lo g _{10} ( x )}{10000000}

Solution steps

- lo g_{10} (2.29 x) \cdot 1 0^{- 7}

Simplify

lo g_{10} (2.29 x) : lo g_{10} (229 x) - 2

= - (lo g_{10} (229 x) - 2) \cdot 1 0^{- 7}

Simplify

- (lo g_{10} (229 x) - 2) \cdot 1 0^{- 7} : - \frac{1}{10000000} lo g_{10} (229) - \frac{lo g _{10} ( x )}{10000000} + \frac{1}{5000000}

= - \frac{1}{10000000} lo g_{10} (229) - \frac{lo g _{10} ( x )}{10000000} + \frac{1}{5000000}

Multiply

\frac{1}{10000000} lo g_{10} (229) : \frac{lo g _{10} ( 229 )}{10000000}

= - \frac{lo g _{10} ( 229 )}{10000000} - \frac{lo g _{10} ( x )}{10000000} + \frac{1}{5000000}

Combine the fractions

- \frac{lo g _{10} ( 229 )}{10000000} - \frac{lo g _{10} ( x )}{10000000} : - \frac{lo g _{10} ( 229 x )}{10000000}

= \frac{1}{5000000} - \frac{lo g _{10} ( 229 x )}{10000000}

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (229 x) = lo g_{10} (229) + lo g_{10} (x)

= \frac{1}{5000000} - \frac{lo g _{10} ( 229 ) + lo g _{10} ( x )}{10000000}

1 e^{- 11}

500 [\frac{( 1 + 0.03 ) ^{24} - 1}{0.03 ( 1 + 0.03 ) ^{24}}] (1 + 0.03)^{- 6}

4.1 \cdot 1 0^{- 8}

e^{- t^{2}} \cdot e^{t^{2}}

4.1 \cdot 1 0^{- 6}

What is simplify-log_{10}(2.29x)10^{-7} ?
The solution to simplify-log_{10}(2.29x)10^{-7} is 1/5000000-(log_{10}(229)+log_{10}(x))/(10000000)