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

The solution to 5log_{4}(a)-10log_{4}(b) is log_{4}((a^5)/(b^{10)})

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simplify 5log_{4}(a)-10log_{4}(b)

simplify

5 lo g_{4} (a) - 10 lo g_{4} (b)

lo g_{4} (\frac{a ^{5}}{b ^{10}})

Solution steps

5 lo g_{4} (a) - 10 lo g_{4} (b)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

\frac{1}{6} lo g_{2} (\frac{1}{6}) + \frac{5}{6} lo g_{2} (\frac{5}{6})

ln (a rc T g (1 + x^{2}))

3 lo g_{10} (x) + lo g_{10} (3)

8 ln (x) - 4 ln (5)

ln (2 e^{y - x})

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