What is 5log_{10}(x)-2log_{10}(4) ?

The solution to 5log_{10}(x)-2log_{10}(4) is log_{10}((x^5)/(16))

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simplify 5log_{10}(x)-2log_{10}(4)

simplify

5 lo g_{10} (x) - 2 lo g_{10} (4)

lo g_{10} (\frac{x ^{5}}{16})

Solution steps

5 lo g_{10} (x) - 2 lo g_{10} (4)

5 lo g_{10} (x) = lo g_{10} (x^{5})

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

= lo g_{10} (x^{5}) - lo g_{10} (4^{2})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (x^{5}) - lo g_{10} (4^{2}) = lo g_{10} (\frac{x ^{5}}{4 ^{2}})

= lo g_{10} (\frac{x ^{5}}{4 ^{2}})

Simplify

\frac{x ^{5}}{4 ^{2}} : \frac{x ^{5}}{16}

= lo g_{10} (\frac{x ^{5}}{16})

\frac{2}{5} + \frac{4}{15}

\frac{3}{4} \cdot 10

\frac{51}{8}

\frac{3}{8} + \frac{5}{7}

(5 x + 7) (5 x - 7)

What is 5log_{10}(x)-2log_{10}(4) ?
The solution to 5log_{10}(x)-2log_{10}(4) is log_{10}((x^5)/(16))