What is 10log_{10}(x)+2/3 log_{10}(64) ?

The solution to 10log_{10}(x)+2/3 log_{10}(64) is log_{10}(16x^{10})

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simplify 10log_{10}(x)+2/3 log_{10}(64)

simplify

10 lo g_{10} (x) + \frac{2}{3} lo g_{10} (64)

lo g_{10} (16 x^{10})

Solution steps

10 lo g_{10} (x) + \frac{2}{3} lo g_{10} (64)

\frac{2}{3} lo g_{10} (64) = 4 lo g_{10} (2)

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

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

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

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

Apply log rule:

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

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

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

Simplify

x^{10} \cdot 2^{4} : x^{10} \cdot 16

= lo g_{10} (x^{10} \cdot 16)

= lo g_{10} (16 x^{10})

\frac{1}{2} ln (x) + 5 ln (y) - 2 ln (z)

\frac{1}{2} lo g_{b} (x) + 2 lo g_{b} (y) - 3 lo g_{b} (x)

lo g_{10} (a b^{3})

lo g_{2} (\frac{y}{8})

What is 10log_{10}(x)+2/3 log_{10}(64) ?
The solution to 10log_{10}(x)+2/3 log_{10}(64) is log_{10}(16x^{10})