What is 5log_{2}(x)+log_{2}(t) ?

The solution to 5log_{2}(x)+log_{2}(t) is log_{2}(x^5t)

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simplify 5log_{2}(x)+log_{2}(t)

simplify

5 lo g_{2} (x) + lo g_{2} (t)

lo g_{2} (x^{5} t)

Solution steps

5 lo g_{2} (x) + lo g_{2} (t)

Apply log rule:

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

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

= lo g_{2} (x^{5}) + lo g_{2} (t)

Apply log rule:

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

lo g_{2} (x^{5}) + lo g_{2} (t) = lo g_{2} (x^{5} t)

= lo g_{2} (x^{5} t)

2 lo g_{6} (x) + 4 lo g_{6} (y)

ln (\frac{1 0 ^{17}}{1 0 ^{18}})

- lo g_{10} (5.5 \cdot 1 0^{- 14})

ln (\frac{5 - 2 6}{2 - 3})

\frac{1}{2} ln (\frac{1}{2}) - \frac{1}{2}

What is 5log_{2}(x)+log_{2}(t) ?
The solution to 5log_{2}(x)+log_{2}(t) is log_{2}(x^5t)