What is simplify-log_{10}(5.3*10^{-5}) ?

The solution to simplify-log_{10}(5.3*10^{-5}) is -log_{10}(5.3)+5

Popular >

simplify-log_{10}(5.3*10^{-5})

simplify

- lo g_{10} (5.3 \cdot 1 0^{- 5})

- lo g_{10} (5.3) + 5

Decimal Notation

4.27572 \dots

Solution steps

- lo g_{10} (5.3 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (5.3 \cdot 1 0^{- 5}) = lo g_{10} (5.3) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (5.3) + lo g_{10} (1 0^{- 5}))

Apply log rule:

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

lo g_{10} (1 0^{- 5}) = - 5 lo g_{10} (10)

= - (lo g_{10} (5.3) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (5.3) - 5)

Distribute parentheses

= - (lo g_{10} (5.3)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (5.3) + 5

- lo g_{10} (3.4 \cdot 1 0^{- 11})

ln (9.5 \cdot 1 0^{- 6})

ln (\frac{e ^{x}}{6 + e ^{x}})

- 3 ln (v - 1) - ln (x)

ln (5 x - 2) 4 - 8 ln (4 - 6 x)

What is simplify-log_{10}(5.3*10^{-5}) ?
The solution to simplify-log_{10}(5.3*10^{-5}) is -log_{10}(5.3)+5