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

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

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

simplify

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

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

Solution steps

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})

= 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)

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

- lo g_{10} (3.2 \cdot 1 0^{- 7})

- \frac{1}{3} ln ∣ x + 2 ∣ + \frac{1}{3} ln ∣ x - 1 ∣

0.082 \cdot ln (0.1 \cdot 0.4)

3 ln (x) + 2 ln (x) - 6 ln (y)

ln (x^{3} y)

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