What is 5log_{2}(m)+4log_{2}(n) ?

The solution to 5log_{2}(m)+4log_{2}(n) is log_{2}(m^5n^4)

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simplify 5log_{2}(m)+4log_{2}(n)

simplify

5 lo g_{2} (m) + 4 lo g_{2} (n)

lo g_{2} (m^{5} n^{4})

Solution steps

5 lo g_{2} (m) + 4 lo g_{2} (n)

Apply log rule:

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

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

= lo g_{2} (m^{5}) + 4 lo g_{2} (n)

Apply log rule:

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

4 lo g_{2} (n) = lo g_{2} (n^{4})

= lo g_{2} (m^{5}) + lo g_{2} (n^{4})

Apply log rule:

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

lo g_{2} (m^{5}) + lo g_{2} (n^{4}) = lo g_{2} (m^{5} n^{4})

= lo g_{2} (m^{5} n^{4})

lo g_{10} (125) + lo g_{10} (25) + lo g_{10} (5)

2 lo g_{10} (4) + 2 lo g_{10} (x)

ln (\frac{x}{x + 2})

5 lo g_{10} (4) - 4 lo g_{10} (x)

ln (72) - ln (3)

What is 5log_{2}(m)+4log_{2}(n) ?
The solution to 5log_{2}(m)+4log_{2}(n) is log_{2}(m^5n^4)