What is log_{7}(32)-log_{7}(8) ?

The solution to log_{7}(32)-log_{7}(8) is 2log_{7}(2)

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simplify log_{7}(32)-log_{7}(8)

simplify

lo g_{7} (32) - lo g_{7} (8)

2 lo g_{7} (2)

Decimal Notation

0.71241 \dots

Solution steps

lo g_{7} (32) - lo g_{7} (8)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{7} (32) - lo g_{7} (8) = lo g_{7} (\frac{32}{8})

= lo g_{7} (\frac{32}{8})

Divide the numbers:

\frac{32}{8} = 4

= lo g_{7} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

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

= 2 lo g_{7} (2)

ln (x) - ln (5)

lo g_{10} (\frac{R ^{5} S ^{4}}{Z ^{6}})

ln (\frac{1}{x + 1})

ln (x) - ln (x - 1)

lo g_{10} (\frac{2 ^{4}}{5})

What is log_{7}(32)-log_{7}(8) ?
The solution to log_{7}(32)-log_{7}(8) is 2log_{7}(2)