What is (log_{10}(2x)+log_{10}(4x^2))/3 ?

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

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simplify (log_{10}(2x)+log_{10}(4x^2))/3

simplify

\frac{lo g _{10} ( 2 x ) + lo g _{10} ( 4 x ^{2} )}{3}

\frac{lo g _{10} ( 8 x ^{3} )}{3}

Solution steps

\frac{lo g _{10} ( 2 x ) + lo g _{10} ( 4 x ^{2} )}{3}

Apply log rule:

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

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

= \frac{lo g _{10} ( 2 x \cdot 4 x ^{2} )}{3}

Simplify

2 x \cdot 4 x^{2} : 8 x^{3}

= \frac{lo g _{10} ( 8 x ^{3} )}{3}

4 ln (θ) + 9 ln (1 - θ)

2 lo g_{b} (2) - lo g_{b} (7) - 4 lo g_{b} (5)

lo g_{10} (30) - lo g_{10} (5)

lo g_{5} (25 (x^{2} - 49))

4 ln (x) + ln (3) - ln (x)

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