What is log_{3}(27(x^2-49)) ?

The solution to log_{3}(27(x^2-49)) is 3+log_{3}(x^2-49)

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simplify log_{3}(27(x^2-49))

simplify

lo g_{3} (27 (x^{2} - 49))

3 + lo g_{3} (x^{2} - 49)

Solution steps

lo g_{3} (27 (x^{2} - 49))

Factor the number:

27 = 3^{3}

= lo g_{3} (3^{3} (x^{2} - 49))

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{3} (3^{3} (x^{2} - 49)) = lo g_{3} (3^{3}) + lo g_{3} (x^{2} - 49)

= lo g_{3} (3^{3}) + lo g_{3} (x^{2} - 49)

Apply log rule:

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

lo g_{3} (3^{3}) = 3

= 3 + lo g_{3} (x^{2} - 49)

lo g_{2} (9) - lo g_{2} (y) + \frac{1}{2} lo g_{2} (x)

\frac{1}{18} ln (\frac{167}{23})

lo g_{10} (A) + lo g_{10} (B) - lo g_{10} (\frac{1}{C})

lo g_{7} (\frac{49 m ^{6}}{k ^{3}})

3.79588 + lo g_{10} (\frac{0.2}{0.5})

What is log_{3}(27(x^2-49)) ?
The solution to log_{3}(27(x^2-49)) is 3+log_{3}(x^2-49)