Question

please help me answer this question.. am giving brainliest​

Answer 1

Step-by-step explanation:

We are going to use the following properties of logarithms to solve this problem:

$\log{\dfrac{a}{b}} = \log{a} - \log{b}$

and

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

So we can rewrite the given equation as

$\log{2x^3} - \log{x} = \log{\left(\dfrac{2x^3}{x}\right)} = \log{2x^2}$

Also,

$\log{16} + \log{x} = \log{(16x)}$

So we can write

$\log{2x^2} = \log{(16x)}$

or eliminating the log symbols, we get

$2x^2 = 16x$

The solutions for the equation above are

$x = 8\:\text{and}\: 0$