What is simplify-log_{10}(4.5\times 10^{-4}) ?

The solution to simplify-log_{10}(4.5\times 10^{-4}) is -log_{10}(4.5)+4

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simplify-log_{10}(4.5\times 10^{-4})

simplify

- lo g_{10} (4.5 \cdot 1 0^{- 4})

- lo g_{10} (4.5) + 4

Decimal Notation

3.34678 \dots

Solution steps

- lo g_{10} (4.5 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (4.5 \cdot 1 0^{- 4}) = lo g_{10} (4.5) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (4.5) + lo g_{10} (1 0^{- 4}))

Apply log rule:

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

lo g_{10} (1 0^{- 4}) = - 4 lo g_{10} (10)

= - (lo g_{10} (4.5) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (4.5) - 4)

Distribute parentheses

= - (lo g_{10} (4.5)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (4.5) + 4

\frac{ln ( \frac{8}{9} )}{2 ln ( 6 )}

ln (x + 8) - ln (x - 8)

ln (e (x))

lo g_{10} (x^{2} + 2 x - 8) - lo g_{10} (x^{2} - 16)

- 6 lo g_{3} (x + 1) + 4 lo g_{3} (2 x)

What is simplify-log_{10}(4.5\times 10^{-4}) ?
The solution to simplify-log_{10}(4.5\times 10^{-4}) is -log_{10}(4.5)+4