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

The solution to 4log_{10}(a)+log_{10}(b) is log_{10}(a^4b)

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simplify 4log_{10}(a)+log_{10}(b)

simplify

4 lo g_{10} (a) + lo g_{10} (b)

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

Solution steps

4 lo g_{10} (a) + lo g_{10} (b)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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