What is log_{b}(2)+2log_{b}(x) ?

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

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simplify log_{b}(2)+2log_{b}(x)

simplify

lo g_{b} (2) + 2 lo g_{b} (x)

lo g_{b} (2 x^{2})

Solution steps

lo g_{b} (2) + 2 lo g_{b} (x)

Apply log rule:

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

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

= lo g_{b} (2) + lo g_{b} (x^{2})

Apply log rule:

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

lo g_{b} (2) + lo g_{b} (x^{2}) = lo g_{b} (2 x^{2})

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

ln (3) (- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4}) + ln (2) (1 - \frac{1}{4} - \frac{3}{4})

ln (1) - ln (\frac{3}{2})

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

lo g_{b} (\frac{x ^{2}}{y ^{3} z ^{4}})

3 lo g_{7} (x) + \frac{1}{3} lo g_{7} (y)

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