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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (z \frac{y}{x})

ln (\frac{25}{360 - 25})

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

ln (1 - i) - ln (1 + i)

ln (\frac{201.5}{200.75})

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