What is expand log_{10}((3xyz^2)^3) ?

The solution to expand log_{10}((3xyz^2)^3) is 3log_{10}(3)+3log_{10}(x)+3log_{10}(y)+6log_{10}(z)

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expand log_{10}((3xyz^2)^3)

expand

lo g_{10} ((3 x y z^{2})^{3})

3 lo g_{10} (3) + 3 lo g_{10} (x) + 3 lo g_{10} (y) + 6 lo g_{10} (z)

Solution steps

lo g_{10} ((3 x y z^{2})^{3})

Apply log rule:

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

lo g_{10} ((3 x y z^{2})^{3}) = 3 lo g_{10} (3 x y z^{2})

= 3 lo g_{10} (3 x y z^{2})

Apply log rule:

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

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

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

Apply log rule:

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

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

= 3 lo g_{10} (3) + 3 lo g_{10} (x) + 3 lo g_{10} (y) + 3 \cdot 2 lo g_{10} (z)

Multiply the numbers:

3 \cdot 2 = 6

= 3 lo g_{10} (3) + 3 lo g_{10} (x) + 3 lo g_{10} (y) + 6 lo g_{10} (z)

ln (\frac{a ^{- 2} b ^{3}}{c ^{- 5}})

\frac{1}{2} lo g_{2} (13)

lo g_{6} (x \cdot y \cdot z^{5})

ln (\frac{x + 6}{e ^{x}})

lo g_{12} (+ \frac{1}{2} lo g_{7} (- lo g_{2} (x)))

What is expand log_{10}((3xyz^2)^3) ?
The solution to expand log_{10}((3xyz^2)^3) is 3log_{10}(3)+3log_{10}(x)+3log_{10}(y)+6log_{10}(z)