What is 4log_{10}(x/5)+log_{10}(625/4) ?

The solution to 4log_{10}(x/5)+log_{10}(625/4) is log_{10}((x^4)/4)

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simplify 4log_{10}(x/5)+log_{10}(625/4)

simplify

4 lo g_{10} (\frac{x}{5}) + lo g_{10} (\frac{625}{4})

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

Solution steps

4 lo g_{10} (\frac{x}{5}) + lo g_{10} (\frac{625}{4})

Apply log rule:

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

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

= lo g_{10} ((\frac{x}{5})^{4}) + lo g_{10} (\frac{625}{4})

Apply log rule:

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

lo g_{10} ((\frac{x}{5})^{4}) + lo g_{10} (\frac{625}{4}) = lo g_{10} ((\frac{x}{5})^{4} \frac{625}{4})

= lo g_{10} ((\frac{x}{5})^{4} \frac{625}{4})

Simplify

(\frac{x}{5})^{4} \frac{625}{4} : \frac{x ^{4}}{4}

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

ln (\frac{2 x ^{2} y}{z ^{4}})

lo g_{5} (3 x + 2) - lo g_{5} (x)

(lo g_{a} (x) - lo g_{a} (y)) + 8 lo g_{a} (v)

lo g_{10} (\frac{64}{z})

\frac{1}{3} lo g_{4} (x) + lo g_{4} (y) - 2

What is 4log_{10}(x/5)+log_{10}(625/4) ?
The solution to 4log_{10}(x/5)+log_{10}(625/4) is log_{10}((x^4)/4)