What is simplify-log_{10}(2*10^{-4}) ?

The solution to simplify-log_{10}(2*10^{-4}) is -log_{10}(2)+4

Popular >

simplify-log_{10}(2*10^{-4})

simplify

- lo g_{10} (2 \cdot 1 0^{- 4})

- lo g_{10} (2) + 4

Decimal Notation

3.69897 \dots

Solution steps

- lo g_{10} (2 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (2 \cdot 1 0^{- 4}) = lo g_{10} (2) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (2) + lo g_{10} (1 0^{- 4}))

Apply log rule:

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

lo g_{10} (1 0^{- 4}) = - 4 lo g_{10} (10)

= - (lo g_{10} (2) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (2) - 4)

Distribute parentheses

= - (lo g_{10} (2)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (2) + 4

- \frac{2}{3} \cdot lo g_{2} (\frac{2}{3}) - \frac{1}{3} \cdot lo g_{2} (\frac{1}{3})

3 lo g_{10} (x) + 2 lo g_{10} (y)

lo g_{5} (8) - lo g_{5} (t)

- lo g_{b} (\frac{1}{4})

lo g_{10} (12) - lo g_{10} (3)

What is simplify-log_{10}(2*10^{-4}) ?
The solution to simplify-log_{10}(2*10^{-4}) is -log_{10}(2)+4