What is 4log_{5}(a)-3/2 log_{5}(b) ?

The solution to 4log_{5}(a)-3/2 log_{5}(b) is log_{5}((a^4)/(b^{3/2)})

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simplify 4log_{5}(a)-3/2 log_{5}(b)

simplify

4 lo g_{5} (a) - \frac{3}{2} lo g_{5} (b)

lo g_{5} (\frac{a ^{4}}{b ^{\frac{3}{2}}})

Solution steps

4 lo g_{5} (a) - \frac{3}{2} lo g_{5} (b)

Apply log rule:

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

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

= lo g_{5} (a^{4}) - \frac{3}{2} lo g_{5} (b)

Apply log rule:

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

\frac{3}{2} lo g_{5} (b) = lo g_{5} (b^{\frac{3}{2}})

= lo g_{5} (a^{4}) - lo g_{5} (b^{\frac{3}{2}})

Apply log rule:

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

lo g_{5} (a^{4}) - lo g_{5} (b^{\frac{3}{2}}) = lo g_{5} (\frac{a ^{4}}{b ^{\frac{3}{2}}})

= lo g_{5} (\frac{a ^{4}}{b ^{\frac{3}{2}}})

lo g_{10} (8) x^{2} - lo g_{10} (2 x)

7 lo g_{10} (z) + 5 lo g_{10} (x) + 3 lo g_{10} (y)

lo g_{b} (\frac{0.34}{0.83})

ln^{2} (a + a^{2} + x^{2}) - ln^{2} (x)

\frac{1}{3} (ln (15) - ln (6))

What is 4log_{5}(a)-3/2 log_{5}(b) ?
The solution to 4log_{5}(a)-3/2 log_{5}(b) is log_{5}((a^4)/(b^{3/2)})