What is 5log_{10}(a)-25log_{10}(b) ?

The solution to 5log_{10}(a)-25log_{10}(b) is log_{10}((a^5)/(b^{25)})

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simplify 5log_{10}(a)-25log_{10}(b)

simplify

5 lo g_{10} (a) - 25 lo g_{10} (b)

lo g_{10} (\frac{a ^{5}}{b ^{25}})

Solution steps

5 lo g_{10} (a) - 25 lo g_{10} (b)

Apply log rule:

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

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

= lo g_{10} (a^{5}) - 25 lo g_{10} (b)

Apply log rule:

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

25 lo g_{10} (b) = lo g_{10} (b^{25})

= lo g_{10} (a^{5}) - lo g_{10} (b^{25})

Apply log rule:

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

lo g_{10} (a^{5}) - lo g_{10} (b^{25}) = lo g_{10} (\frac{a ^{5}}{b ^{25}})

= lo g_{10} (\frac{a ^{5}}{b ^{25}})

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

\frac{2}{3} lo g_{b} (27) + 2 lo g_{b} (2) - lo g_{b} (3)

- \frac{8}{12} lo g_{2} (\frac{8}{12}) - \frac{4}{12} lo g_{2} (\frac{4}{12})

ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1

lo g_{10} (12 x) - lo g_{10} (3 x)

What is 5log_{10}(a)-25log_{10}(b) ?
The solution to 5log_{10}(a)-25log_{10}(b) is log_{10}((a^5)/(b^{25)})