What is 1/2 log_{10}(16x^4)+log_{10}(2x) ?

The solution to 1/2 log_{10}(16x^4)+log_{10}(2x) is log_{10}(8x^3)

Popular >

simplify 1/2 log_{10}(16x^4)+log_{10}(2x)

simplify

\frac{1}{2} lo g_{10} (16 x^{4}) + lo g_{10} (2 x)

lo g_{10} (8 x^{3})

Solution steps

\frac{1}{2} lo g_{10} (16 x^{4}) + lo g_{10} (2 x)

Apply log rule:

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

\frac{1}{2} lo g_{10} (16 x^{4}) = lo g_{10} ((16 x^{4})^{\frac{1}{2}})

= lo g_{10} ((16 x^{4})^{\frac{1}{2}}) + lo g_{10} (2 x)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} ((16 x^{4})^{\frac{1}{2}}) + lo g_{10} (2 x) = lo g_{10} ((16 x^{4})^{\frac{1}{2}} \cdot 2 x)

= lo g_{10} ((16 x^{4})^{\frac{1}{2}} \cdot 2 x)

Simplify

(16 x^{4})^{\frac{1}{2}} \cdot 2 x : 8 x^{3}

= lo g_{10} (8 x^{3})

lo g_{a} (26) + lo g_{a} (4)

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

3 ln (3) - 2 ln (2)

ln (x + 1) - ln (x - 4)

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

What is 1/2 log_{10}(16x^4)+log_{10}(2x) ?
The solution to 1/2 log_{10}(16x^4)+log_{10}(2x) is log_{10}(8x^3)