What is simplify-log_{10}(1x10^{-7}) ?

The solution to simplify-log_{10}(1x10^{-7}) is -log_{10}(x)+7

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simplify-log_{10}(1x10^{-7})

simplify

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

- lo g_{10} (x) + 7

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= - (lo g_{10} (1) + lo g_{10} (x) - 7 lo g_{10} (10))

lo g_{10} (1) = 0

7 lo g_{10} (10) = 7

= - (lo g_{10} (x) + 0 - 7)

Simplify

0 + lo g_{10} (x) - 7 : lo g_{10} (x) - 7

= - (lo g_{10} (x) - 7)

Distribute parentheses

= - (lo g_{10} (x)) - (- 7)

Apply minus-plus rules

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

= - lo g_{10} (x) + 7

\frac{1}{4} lo g_{c} (x) + 5 lo g_{c} (y) - 4 lo g_{c} (x)

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

lo g_{9} (x + 3) + lo g_{9} (x - 5)

\frac{1}{2} ln (- 1)

lo g_{2} (5 x)

What is simplify-log_{10}(1x10^{-7}) ?
The solution to simplify-log_{10}(1x10^{-7}) is -log_{10}(x)+7