What is 2log_{b}(t)+1/2 log_{b}(r) ?

The solution to 2log_{b}(t)+1/2 log_{b}(r) is log_{b}(t^2r^{1/2})

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simplify 2log_{b}(t)+1/2 log_{b}(r)

simplify

2 lo g_{b} (t) + \frac{1}{2} lo g_{b} (r)

lo g_{b} (t^{2} r^{\frac{1}{2}})

Solution steps

2 lo g_{b} (t) + \frac{1}{2} lo g_{b} (r)

Apply log rule:

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

2 lo g_{b} (t) = lo g_{b} (t^{2})

= lo g_{b} (t^{2}) + \frac{1}{2} lo g_{b} (r)

Apply log rule:

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

\frac{1}{2} lo g_{b} (r) = lo g_{b} (r^{\frac{1}{2}})

= lo g_{b} (t^{2}) + lo g_{b} (r^{\frac{1}{2}})

Apply log rule:

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

lo g_{b} (t^{2}) + lo g_{b} (r^{\frac{1}{2}}) = lo g_{b} (t^{2} r^{\frac{1}{2}})

= lo g_{b} (t^{2} r^{\frac{1}{2}})

lo g_{7} (x) + 2 lo g_{7} (y)

ln (3) + 2 ln (2)

3 lo g_{10} (a) - 2 lo g_{10} (b)

ln^{2} (\frac{1}{4})

ln (\frac{( x - 3 ) ^{4} x}{x + 1})

What is 2log_{b}(t)+1/2 log_{b}(r) ?
The solution to 2log_{b}(t)+1/2 log_{b}(r) is log_{b}(t^2r^{1/2})