What is simplify-log_{10}(3.9(10^{-8})) ?

The solution to simplify-log_{10}(3.9(10^{-8})) is -log_{10}(3.9)+8

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simplify-log_{10}(3.9(10^{-8}))

simplify

- lo g_{10} (3.9 (1 0^{- 8}))

- lo g_{10} (3.9) + 8

Decimal Notation

7.40893 \dots

Solution steps

- lo g_{10} (3.9 (1 0^{- 8}))

Apply log rule:

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

lo g_{10} (3.9 (1 0^{- 8})) = lo g_{10} (3.9) + lo g_{10} (1 0^{- 8})

= - (lo g_{10} (3.9) + lo g_{10} (1 0^{- 8}))

Apply log rule:

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

lo g_{10} (1 0^{- 8}) = - 8 lo g_{10} (10)

= - (lo g_{10} (3.9) - 8 lo g_{10} (10))

8 lo g_{10} (10) = 8

= - (lo g_{10} (3.9) - 8)

Distribute parentheses

= - (lo g_{10} (3.9)) - (- 8)

Apply minus-plus rules

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

= - lo g_{10} (3.9) + 8

lo g_{10} \frac{( b ^{3} )}{a ^{5} c ^{8}}

ln (2 n^{3} + 2) - ln (5 n^{3} + 2 n^{2} + 4)

2 ln (t) + ln^{2} (t)

4 - \frac{5}{2} ln (5) - \frac{11}{8} + \frac{5}{2} ln (2)

lo g_{10} (\frac{x ^{2} - 4}{( x + 3 ) ^{2}})

What is simplify-log_{10}(3.9(10^{-8})) ?
The solution to simplify-log_{10}(3.9(10^{-8})) is -log_{10}(3.9)+8