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

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

Popular >

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

simplify

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

- lo g_{10} (2) + 10

Decimal Notation

9.69897 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

10 lo g_{10} (10) = 10

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

Distribute parentheses

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

Apply minus-plus rules

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

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

lo g_{10} (\frac{5 x}{3})

2 ln (6 x) - \frac{2}{3} ln (x^{3})

lo g_{4} (5) + lo g_{4} (12) - lo g_{4} (3.75)

lo g_{7} (49 x^{5})

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

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