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

The solution to 5log_{10}(4)-4log_{10}(x) is log_{10}((1024)/(x^4))

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

simplify

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

lo g_{10} (\frac{1024}{x ^{4}})

Solution steps

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

5 lo g_{10} (4) = lo g_{10} (4^{5})

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

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

Apply log rule:

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

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

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

Simplify

\frac{4 ^{5}}{x ^{4}} : \frac{1024}{x ^{4}}

= lo g_{10} (\frac{1024}{x ^{4}})

ln (72) - ln (3)

lo g_{10} (\frac{a ^{2}}{b})

ln (\frac{2 x - 5}{cos ^{2} ( 3 x )})

\frac{1}{- 0.0001216} ln (\frac{2}{5})

\frac{3}{8} lo g_{2} (\frac{3}{8}) + \frac{5}{8} lo g_{2} (\frac{5}{8})

What is 5log_{10}(4)-4log_{10}(x) ?
The solution to 5log_{10}(4)-4log_{10}(x) is log_{10}((1024)/(x^4))