What is 1/2 log_{10}(9)+3log_{10}(2) ?

The solution to 1/2 log_{10}(9)+3log_{10}(2) is log_{10}(24)

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simplify 1/2 log_{10}(9)+3log_{10}(2)

simplify

\frac{1}{2} lo g_{10} (9) + 3 lo g_{10} (2)

lo g_{10} (24)

Decimal Notation

1.38021 \dots

Solution steps

\frac{1}{2} lo g_{10} (9) + 3 lo g_{10} (2)

\frac{1}{2} lo g_{10} (9) = lo g_{10} (3)

= lo g_{10} (3) + 3 lo g_{10} (2)

Apply log rule:

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

3 lo g_{10} (2) = lo g_{10} (2^{3})

= lo g_{10} (3) + lo g_{10} (2^{3})

Apply log rule:

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

lo g_{10} (3) + lo g_{10} (2^{3}) = lo g_{10} (3 \cdot 2^{3})

= lo g_{10} (3 \cdot 2^{3})

3 \cdot 2^{3} = 24

= lo g_{10} (24)

- \frac{1}{3} ln (8) + 2 ln (5)

\frac{1}{2} ln (x) + 8 ln (y) - 7 ln (z)

7 lo g_{b} (x) + 3 lo g_{b} (z)

lo g_{10} (A) - lo g_{10} (B)

lo g_{10} (\frac{x ^{2} ( 1 + x ^{2} ) ^{2}}{( 1 - x ^{2} ) ^{2}})

What is 1/2 log_{10}(9)+3log_{10}(2) ?
The solution to 1/2 log_{10}(9)+3log_{10}(2) is log_{10}(24)