What is simplify-log_{10}(x*10^{-n}) ?

The solution to simplify-log_{10}(x*10^{-n}) is -log_{10}(x)+n

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simplify-log_{10}(x*10^{-n})

simplify

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

- lo g_{10} (x) + n

Solution steps

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

Apply log rule:

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

lo g_{10} (x \cdot 1 0^{- n}) = lo g_{10} (x) + lo g_{10} (1 0^{- n})

= - (lo g_{10} (x) + lo g_{10} (1 0^{- n}))

Apply log rule:

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

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

= - (lo g_{10} (x) - n lo g_{10} (10))

n lo g_{10} (10) = n

= - (lo g_{10} (x) - n)

Distribute parentheses

= - (lo g_{10} (x)) - (- n)

Apply minus-plus rules

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

= - lo g_{10} (x) + n

\frac{( ln ( x ) - ln ( y ) )}{x}

- lo g_{10} (0.39 \cdot 1 0^{- 3})

ln (\frac{y}{x ^{4}})

- lo g_{10} (4.12 \cdot 1 0^{- 3})

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

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