What is simplify-log_{10}(5.1*10^{-3}) ?

The solution to simplify-log_{10}(5.1*10^{-3}) is -log_{10}(5.1)+3

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simplify-log_{10}(5.1*10^{-3})

simplify

- lo g_{10} (5.1 \cdot 1 0^{- 3})

- lo g_{10} (5.1) + 3

Decimal Notation

2.29242 \dots

Solution steps

- lo g_{10} (5.1 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (5.1 \cdot 1 0^{- 3}) = lo g_{10} (5.1) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (5.1) + 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} (5.1) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (5.1) - 3)

Distribute parentheses

= - (lo g_{10} (5.1)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (5.1) + 3

ln (2 e^{(\frac{π}{4})^{2}})

- \frac{4 ln ( 11 )}{ln ( 2 )}

\frac{ln ( \frac{27}{16} )}{6 ln ( 3 )}

\frac{2 ln ( 2 ) - 2}{4 ln ( 2 )}

ln (\frac{0.0167}{0.000124})

What is simplify-log_{10}(5.1*10^{-3}) ?
The solution to simplify-log_{10}(5.1*10^{-3}) is -log_{10}(5.1)+3