What is 2log_{7}(u)+4log_{7}(v) ?

The solution to 2log_{7}(u)+4log_{7}(v) is log_{7}(u^2v^4)

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simplify 2log_{7}(u)+4log_{7}(v)

simplify

2 lo g_{7} (u) + 4 lo g_{7} (v)

lo g_{7} (u^{2} v^{4})

Solution steps

2 lo g_{7} (u) + 4 lo g_{7} (v)

Apply log rule:

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

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

= lo g_{7} (u^{2}) + 4 lo g_{7} (v)

Apply log rule:

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

4 lo g_{7} (v) = lo g_{7} (v^{4})

= lo g_{7} (u^{2}) + lo g_{7} (v^{4})

Apply log rule:

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

lo g_{7} (u^{2}) + lo g_{7} (v^{4}) = lo g_{7} (u^{2} v^{4})

= lo g_{7} (u^{2} v^{4})

ln (x + y) - ln (x)

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

5 lo g_{10} (a) - lo g_{10} (b) + 3 lo g_{10} (c)

lo g_{t} (M) + lo g_{t} (N)

- \frac{11}{20} lo g_{2} (\frac{11}{20}) - \frac{9}{20} lo g_{2} (\frac{9}{20})

What is 2log_{7}(u)+4log_{7}(v) ?
The solution to 2log_{7}(u)+4log_{7}(v) is log_{7}(u^2v^4)