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

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

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

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

lo g_{10} (2) - lo g_{10} (14)

lo g_{2} (x^{2} - 3 x + 2) - lo g_{2} (x - 1)

2 lo g_{10} (5) - lo g_{10} (15) + lo g_{10} (9)

lo g_{3} (\frac{3}{y})

lo g_{x} (x y)

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