What is 3log_{10}(x+1)+log_{10}(4x+7) ?

The solution to 3log_{10}(x+1)+log_{10}(4x+7) is log_{10}((x+1)^3(4x+7))

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simplify 3log_{10}(x+1)+log_{10}(4x+7)

simplify

3 lo g_{10} (x + 1) + lo g_{10} (4 x + 7)

lo g_{10} ((x + 1)^{3} (4 x + 7))

Solution steps

3 lo g_{10} (x + 1) + lo g_{10} (4 x + 7)

Apply log rule:

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

3 lo g_{10} (x + 1) = lo g_{10} ((x + 1)^{3})

= lo g_{10} ((x + 1)^{3}) + lo g_{10} (4 x + 7)

Apply log rule:

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

lo g_{10} ((x + 1)^{3}) + lo g_{10} (4 x + 7) = lo g_{10} ((x + 1)^{3} (4 x + 7))

= lo g_{10} ((x + 1)^{3} (4 x + 7))

lo g_{10} (\frac{7 a}{8})

lo g_{3} (1 2^{\frac{5}{6}}) x^{9}

lo g_{5} (\frac{x}{125})

ln (\frac{e ^{5}}{4})

ln (ln (y)) + ln (y)

What is 3log_{10}(x+1)+log_{10}(4x+7) ?
The solution to 3log_{10}(x+1)+log_{10}(4x+7) is log_{10}((x+1)^3(4x+7))