What is 1+2log_{10}(a)+log_{10}(b) ?

The solution to 1+2log_{10}(a)+log_{10}(b) is 1+log_{10}(a^2b)

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simplify 1+2log_{10}(a)+log_{10}(b)

simplify

1 + 2 lo g_{10} (a) + lo g_{10} (b)

1 + lo g_{10} (a^{2} b)

Solution steps

1 + 2 lo g_{10} (a) + 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})

= 1 + lo g_{10} (a^{2}) + lo g_{10} (b)

Apply log rule:

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

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

= 1 + lo g_{10} (a^{2} b)

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What is 1+2log_{10}(a)+log_{10}(b) ?
The solution to 1+2log_{10}(a)+log_{10}(b) is 1+log_{10}(a^2b)