What is simplify-log_{10}(2.14*10^{-2}) ?

The solution to simplify-log_{10}(2.14*10^{-2}) is -log_{10}(2.14)+2

Popular >

simplify-log_{10}(2.14*10^{-2})

simplify

- lo g_{10} (2.14 \cdot 1 0^{- 2})

- lo g_{10} (2.14) + 2

Decimal Notation

1.66958 \dots

Solution steps

- lo g_{10} (2.14 \cdot 1 0^{- 2})

Apply log rule:

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

lo g_{10} (2.14 \cdot 1 0^{- 2}) = lo g_{10} (2.14) + lo g_{10} (1 0^{- 2})

= - (lo g_{10} (2.14) + 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} (2.14) - 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (2.14) - 2)

Distribute parentheses

= - (lo g_{10} (2.14)) - (- 2)

Apply minus-plus rules

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

= - lo g_{10} (2.14) + 2

- 5 ln (\frac{0.01}{0.9})

lo g_{7} (13.3) - lo g_{7} (1.9)

- lo g_{10} (6.2 \cdot 1 0^{- 3})

ln (x) - 4 (ln (x - 2) + ln (x + 2))

ln (5 \cdot 1 0^{4})

What is simplify-log_{10}(2.14*10^{-2}) ?
The solution to simplify-log_{10}(2.14*10^{-2}) is -log_{10}(2.14)+2