What is 2log_{10}(a)-4log_{10}(b) ?

The solution to 2log_{10}(a)-4log_{10}(b) is log_{10}((a^2)/(b^4))

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simplify 2log_{10}(a)-4log_{10}(b)

simplify

2 lo g_{10} (a) - 4 lo g_{10} (b)

lo g_{10} (\frac{a ^{2}}{b ^{4}})

Solution steps

2 lo g_{10} (a) - 4 lo g_{10} (b)

Apply log rule:

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

2 lo g_{10} (a) = lo g_{10} (a^{2})

= lo g_{10} (a^{2}) - 4 lo g_{10} (b)

Apply log rule:

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

4 lo g_{10} (b) = lo g_{10} (b^{4})

= lo g_{10} (a^{2}) - lo g_{10} (b^{4})

Apply log rule:

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

lo g_{10} (a^{2}) - lo g_{10} (b^{4}) = lo g_{10} (\frac{a ^{2}}{b ^{4}})

= lo g_{10} (\frac{a ^{2}}{b ^{4}})

lo g_{5} (4 x^{2})

lo g_{b} (x^{2}) y^{3}

lo g_{5} (\frac{5 x ^{7}}{y})

[ln (x^{5} - 1) - ln (x^{3} - 1)]

What is 2log_{10}(a)-4log_{10}(b) ?
The solution to 2log_{10}(a)-4log_{10}(b) is log_{10}((a^2)/(b^4))