What is expand log_{7}(a^2b^3c) ?

The solution to expand log_{7}(a^2b^3c) is 2log_{7}(a)+3log_{7}(b)+log_{7}(c)

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expand log_{7}(a^2b^3c)

expand

lo g_{7} (a^{2} b^{3} c)

2 lo g_{7} (a) + 3 lo g_{7} (b) + lo g_{7} (c)

Solution steps

lo g_{7} (a^{2} b^{3} c)

Apply log rule:

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

lo g_{7} (a^{2} b^{3} c) = lo g_{7} (a^{2}) + lo g_{7} (b^{3}) + lo g_{7} (c)

= lo g_{7} (a^{2}) + lo g_{7} (b^{3}) + lo g_{7} (c)

Apply log rule:

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

lo g_{7} (a^{2}) = 2 lo g_{7} (a)

= 2 lo g_{7} (a) + lo g_{7} (b^{3}) + lo g_{7} (c)

Apply log rule:

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

lo g_{7} (b^{3}) = 3 lo g_{7} (b)

= 2 lo g_{7} (a) + 3 lo g_{7} (b) + lo g_{7} (c)

38 ln (\frac{38}{21.21})

- 2 ln (5 x)

0.026 \cdot ln (\frac{0.4114}{8 \cdot 1 0 ^{- 16}})

ln (2) - 2 ln (2 + 1)

ln (a) - 4 ln (b) + 5 ln (c)

What is expand log_{7}(a^2b^3c) ?
The solution to expand log_{7}(a^2b^3c) is 2log_{7}(a)+3log_{7}(b)+log_{7}(c)