Question

Which is 3 logx + 4 log(x-2) written as a single logarithm?

Answer 1

Answer:

The answer is $12\log{(x(x-2))}$

Step-by-step explanation:

Exponential property of logarithm:

We have that:

$a \log{x} = \log{x^{a}}$

Sum of logarithms:

We have that:

$\log{a} + \log{b} = \log{ab}$

Applying the exponential property:

$3\log{x} = \log{x^3}$

$4\log{(x-2)} = \log{(x-2)^4}$

So

$3\log{x} + 4\log{x-2} = \log{x^3} + \log{(x-2)^4}$

Additive property

$\log{x^3} + \log{(x-2)^4} = \log{x^3(x-2)^4} = \log{(x(x-2))^12}$

Exponential property:

$\log{(x(x-2))^12} = 12\log{(x(x-2))}$

The answer is $12\log{(x(x-2))}$