What is expand log_{5}((a^3)/(b^2)) ?

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

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expand log_{5}((a^3)/(b^2))

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{5} (a^{3}) = 3 lo g_{5} (a)

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

Apply log rule:

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

lo g_{5} (b^{2}) = 2 lo g_{5} (b)

= 3 lo g_{5} (a) - 2 lo g_{5} (b)

ln (4 e^{6})

lo g_{10} (2 x - 7) - lo g_{10} (x - 1)

lo g_{b} (\frac{p ^{4} q ^{7}}{m ^{4} b ^{7}})

2 ln (5) + ln (6)

lo g_{3} (x) - lo g_{3} (x^{7})

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