What is simplify-log_{10}(4*10^{-15}) ?

The solution to simplify-log_{10}(4*10^{-15}) is -2log_{10}(2)+15

Popular >

simplify-log_{10}(4*10^{-15})

simplify

- lo g_{10} (4 \cdot 1 0^{- 15})

- 2 lo g_{10} (2) + 15

Decimal Notation

14.39794 \dots

Solution steps

- lo g_{10} (4 \cdot 1 0^{- 15})

Apply log rule:

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

lo g_{10} (4 \cdot 1 0^{- 15}) = lo g_{10} (4) + lo g_{10} (1 0^{- 15})

= - (lo g_{10} (4) + lo g_{10} (1 0^{- 15}))

Apply log rule:

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

lo g_{10} (1 0^{- 15}) = - 15 lo g_{10} (10)

= - (lo g_{10} (4) - 15 lo g_{10} (10))

15 lo g_{10} (10) = 15

= - (lo g_{10} (4) - 15)

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

= - (2 lo g_{10} (2) - 15)

Distribute parentheses

= - (2 lo g_{10} (2)) - (- 15)

Apply minus-plus rules

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

= - 2 lo g_{10} (2) + 15

8.314 (59 + 273) ln (0.286) - ln (1.99 \cdot 1 0^{11})

- lo g_{10} (7.2 \cdot 1 0^{- 5})

2 ln (- 1) - 2 ln (- 2)

ln \frac{( \frac{( - \frac{4}{3} )}{( - \frac{7}{6} )} )}{2}

2 ln (2) + 3 ln (3)

What is simplify-log_{10}(4*10^{-15}) ?
The solution to simplify-log_{10}(4*10^{-15}) is -2log_{10}(2)+15