What is simplify-log_{10}(1.02*10^{-2}) ?

The solution to simplify-log_{10}(1.02*10^{-2}) is -log_{10}(1.02)+2

Popular >

simplify-log_{10}(1.02*10^{-2})

simplify

- lo g_{10} (1.02 \cdot 1 0^{- 2})

- lo g_{10} (1.02) + 2

Decimal Notation

1.99139 \dots

Solution steps

- lo g_{10} (1.02 \cdot 1 0^{- 2})

Apply log rule:

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

lo g_{10} (1.02 \cdot 1 0^{- 2}) = lo g_{10} (1.02) + lo g_{10} (1 0^{- 2})

= - (lo g_{10} (1.02) + 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} (1.02) - 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (1.02) - 2)

Distribute parentheses

= - (lo g_{10} (1.02)) - (- 2)

Apply minus-plus rules

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

= - lo g_{10} (1.02) + 2

\frac{1}{8} (ln (x + 4) - ln (x - 4)) + c

ln (3) + ln (7) - ln (2) - 2 ln (4)

ln (\frac{4 x ^{4} + 4 x}{x ^{2} + 2 x})

- (\frac{5}{6}) lo g_{2} (\frac{5}{6}) - (\frac{1}{6}) lo g_{2} (\frac{1}{6})

ln (\frac{2}{6})

What is simplify-log_{10}(1.02*10^{-2}) ?
The solution to simplify-log_{10}(1.02*10^{-2}) is -log_{10}(1.02)+2