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

The solution to 5log_{10}(a)+25log_{10}(b) is log_{10}(a^5b^{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} (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} (ab)

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

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

4 ln (x) - \frac{1}{5} ln (y)

lo g_{10} (\frac{3 x}{7})

lo g_{5} (\frac{25}{x + 7})

lo g_{a} (\frac{a B}{C ^{4}})

lo g_{10} (\frac{( 1 + x )}{( 1 - x )})

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