What is 3log_{7}(x)+2log_{7}(z) ?

The solution to 3log_{7}(x)+2log_{7}(z) is log_{7}(x^3z^2)

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simplify 3log_{7}(x)+2log_{7}(z)

simplify

3 lo g_{7} (x) + 2 lo g_{7} (z)

lo g_{7} (x^{3} z^{2})

Solution steps

3 lo g_{7} (x) + 2 lo g_{7} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{7} (x^{3}) + 2 lo g_{7} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{7} (x^{3}) + lo g_{7} (z^{2})

Apply log rule:

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

lo g_{7} (x^{3}) + lo g_{7} (z^{2}) = lo g_{7} (x^{3} z^{2})

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

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

ln (\frac{75}{49})

ln (ln (\frac{1}{1 - 0.02})) - ln (ln (\frac{1}{1 - 0.003}))

2.45 + lo g_{10} (\frac{0.022}{0.069})

(0.287) ln (\frac{500}{200})

What is 3log_{7}(x)+2log_{7}(z) ?
The solution to 3log_{7}(x)+2log_{7}(z) is log_{7}(x^3z^2)