What is simplify-log_{10}(9.2*10^{-2}) ?

The solution to simplify-log_{10}(9.2*10^{-2}) is -log_{10}(9.2)+2

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simplify-log_{10}(9.2*10^{-2})

simplify

- lo g_{10} (9.2 \cdot 1 0^{- 2})

- lo g_{10} (9.2) + 2

Decimal Notation

1.03621 \dots

Solution steps

- lo g_{10} (9.2 \cdot 1 0^{- 2})

Apply log rule:

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

lo g_{10} (9.2 \cdot 1 0^{- 2}) = lo g_{10} (9.2) + lo g_{10} (1 0^{- 2})

= - (lo g_{10} (9.2) + lo g_{10} (1 0^{- 2}))

Apply log rule:

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

lo g_{10} (1 0^{- 2}) = - 2 lo g_{10} (10)

= - (lo g_{10} (9.2) - 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (9.2) - 2)

Distribute parentheses

= - (lo g_{10} (9.2)) - (- 2)

Apply minus-plus rules

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

= - lo g_{10} (9.2) + 2

ln (2 x) + ln (y^{2})

- 3 ln ∣ x + 4 ∣ + 3 ln ∣ x - 4 ∣ + 2 C

ln (x - 2^{\frac{3}{2}} - 2) - ln (x + 2^{\frac{3}{2}} - 2)

- \frac{1}{3} ln (\frac{1}{10000000000000})

4.53759 + lo g_{10} (\frac{0.51}{0.16})

What is simplify-log_{10}(9.2*10^{-2}) ?
The solution to simplify-log_{10}(9.2*10^{-2}) is -log_{10}(9.2)+2