What is expand log_{7}((2^3)/(5^2)) ?

The solution to expand log_{7}((2^3)/(5^2)) is 3log_{7}(2)-2log_{7}(5)

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expand log_{7}((2^3)/(5^2))

expand

lo g_{7} (\frac{2 ^{3}}{5 ^{2}})

3 lo g_{7} (2) - 2 lo g_{7} (5)

Decimal Notation

- 0.58555 \dots

Solution steps

lo g_{7} (\frac{2 ^{3}}{5 ^{2}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{7} (\frac{2 ^{3}}{5 ^{2}}) = lo g_{7} (2^{3}) - lo g_{7} (5^{2})

= lo g_{7} (2^{3}) - lo g_{7} (5^{2})

Apply log rule:

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

lo g_{7} (2^{3}) = 3 lo g_{7} (2)

= 3 lo g_{7} (2) - lo g_{7} (5^{2})

Apply log rule:

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

lo g_{7} (5^{2}) = 2 lo g_{7} (5)

= 3 lo g_{7} (2) - 2 lo g_{7} (5)

- lo g_{10} (1.124 \cdot 1 0^{- 6})

2 lo g_{6} (x) + \frac{1}{2} lo g_{6} (y) - 2 - 7 lo g_{6} (z)

lo g_{2} (75) - 2 lo g_{2} (5)

ln (x) + ln (x + 8)

What is expand log_{7}((2^3)/(5^2)) ?
The solution to expand log_{7}((2^3)/(5^2)) is 3log_{7}(2)-2log_{7}(5)