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})

ln (15 x)

ln (\frac{a ^{2}}{b}) + ln (ab) + ln (a^{3})

ln (x \times y)

lo g_{3} (\frac{7}{13})

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})