What is log_{2}(6x) ?

The solution to log_{2}(6x) is 1+log_{2}(3)+log_{2}(x)

Popular >

simplify log_{2}(6x)

simplify

lo g_{2} (6 x)

1 + lo g_{2} (3) + lo g_{2} (x)

Solution steps

lo g_{2} (6 x)

Factor the number:

6 = 2 \cdot 3

= lo g_{2} (2 \cdot 3 x)

Apply log rule:

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

lo g_{2} (2 \cdot 3 x) = lo g_{2} (2) + lo g_{2} (3 x)

= lo g_{2} (2) + lo g_{2} (3 x)

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= 1 + lo g_{2} (3 x)

Apply log rule:

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

lo g_{2} (3 x) = lo g_{2} (3) + lo g_{2} (x)

= 1 + (lo g_{2} (3) + lo g_{2} (x))

Apply rule:

a + (b + c) = a + b + c

1 + (lo g_{2} (3) + lo g_{2} (x)) = 1 + lo g_{2} (3) + lo g_{2} (x)

= 1 + lo g_{2} (3) + lo g_{2} (x)

lo g_{10} (x) - \frac{1}{2} lo g_{10} (y) + 4 lo g_{10} (z)

tanh (\frac{1}{2} lo g_{10} (\frac{1 + z}{1 - z}))

\frac{1}{2} lo g_{10} (x) + \frac{1}{2} lo g_{10} (y)

lo g_{10} (\frac{27 a}{b})

ln (\frac{x}{x - 4}) + ln (\frac{x + 4}{x}) - ln (x^{2} - 16)