What is 2log_{5}(a)+4log_{5}(b) ?

The solution to 2log_{5}(a)+4log_{5}(b) is log_{5}(a^2b^4)

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simplify 2log_{5}(a)+4log_{5}(b)

simplify

2 lo g_{5} (a) + 4 lo g_{5} (b)

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

Solution steps

2 lo g_{5} (a) + 4 lo g_{5} (b)

Apply log rule:

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

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

= lo g_{5} (a^{2}) + 4 lo g_{5} (b)

Apply log rule:

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

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

= lo g_{5} (a^{2}) + lo g_{5} (b^{4})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{5} (a^{2}) + lo g_{5} (b^{4}) = lo g_{5} (a^{2} b^{4})

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

lo g_{a} (\frac{x ^{3} y}{z})

3 ln (9) - 2 ln (6) - ln (3)

lo g_{4} (\frac{64}{x - 1})

lo g_{10} (15) - lo g_{10} (3)

- \frac{1}{3} lo g_{2} (\frac{1}{3}) - \frac{2}{3} lo g_{2} (\frac{2}{3})

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