What is simplify-2(log_{10}(15)+1/2*log_{10}(1/9)) ?

The solution to simplify-2(log_{10}(15)+1/2*log_{10}(1/9)) is -2log_{10}(5)

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simplify-2(log_{10}(15)+1/2*log_{10}(1/9))

simplify

- 2 (lo g_{10} (15) + \frac{1}{2} \cdot lo g_{10} (\frac{1}{9}))

- 2 lo g_{10} (5)

Decimal Notation

- 1.39794 \dots

Solution steps

- 2 (lo g_{10} (15) + \frac{1}{2} lo g_{10} (\frac{1}{9}))

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

\frac{1}{2} lo g_{10} (\frac{1}{9}) = lo g_{10} ((\frac{1}{9})^{\frac{1}{2}})

= - 2 (lo g_{10} (15) + lo g_{10} ((\frac{1}{9})^{\frac{1}{2}}))

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (15) + lo g_{10} ((\frac{1}{9})^{\frac{1}{2}}) = lo g_{10} (15 (\frac{1}{9})^{\frac{1}{2}})

= - 2 lo g_{10} (15 (\frac{1}{9})^{\frac{1}{2}})

Simplify

15 (\frac{1}{9})^{\frac{1}{2}} : 5

= - 2 lo g_{10} (5)

lo g_{3} (x) - lo g_{3} (x^{8})

6 lo g_{8} (11) - 30 lo g_{8} (3)

lo g_{a} (x^{2}) + 3 lo g_{a} (x) - 2 lo g_{a} (4 x)

3 ln (3) + 3 ln (y)

What is simplify-2(log_{10}(15)+1/2*log_{10}(1/9)) ?
The solution to simplify-2(log_{10}(15)+1/2*log_{10}(1/9)) is -2log_{10}(5)