What is 8log_{e}(2x)-log_{e}(2) ?

The solution to 8log_{e}(2x)-log_{e}(2) is ln(128x^8)

Popular >

simplify 8log_{e}(2x)-log_{e}(2)

simplify

8 lo g_{e} (2 x) - lo g_{e} (2)

ln (128 x^{8})

Solution steps

8 lo g_{e} (2 x) - lo g_{e} (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

8 lo g_{e} (2 x) = lo g_{e} ((2 x)^{8})

= lo g_{e} ((2 x)^{8}) - lo g_{e} (2)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{e} ((2 x)^{8}) - lo g_{e} (2) = lo g_{e} (\frac{( 2 x ) ^{8}}{2})

= lo g_{e} (\frac{( 2 x ) ^{8}}{2})

Simplify

\frac{( 2 x ) ^{8}}{2} : 128 x^{8}

= lo g_{e} (128 x^{8})

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (128 x^{8})

lo g_{2} ((x^{3} + 2) (x - 4)^{3})

lo g_{10} (5 \cdot 1 0^{- 3})

ln ((x + 1)^{2} m)

ln (2 n) + 3 ln (b) n - ln (π) n - 2 ln (b^{2} + (x - a)^{2})

lo g_{10} (\frac{x ^{2} y ^{5}}{z ^{3}})

What is 8log_{e}(2x)-log_{e}(2) ?
The solution to 8log_{e}(2x)-log_{e}(2) is ln(128x^8)