[Math] how to simplify log base 2 and log base 4

Question

How do I simplify the following expression:

$$\log_2(2x+1) – 5\log_4(x^2) + 4\log_2(x)$$

That's it, please help me ok?

Answer 1

$\log_2(2x+1)-5\log_4x^2+4\log_2x$

$=\log_2(2x+1)+\log_2x^4-5\frac{\log_yx^2}{\log_y4}$

as $\log a+ \log b=\log ab,m\log a=\log a^m$ and $\log_yz=\frac{\log_xz}{\log_xy}$ where $x\neq 1$ as $\log_1y$ is not defined.

$=\log_2(2x+1)x^4-5\frac{\log_yx^2}{\log_y2^2}$

$=\log_2(2x+1)x^4-5\frac{2\log_yx}{2\log_y2}$

$=\log_2(2x+1)x^4-5\log_2x$

$=\log_2(2x+1)x^4-\log_2x^5$

$=\log_2\frac{(2x+1)x^4}{x^5}$

$=\log_2\frac{(2x+1)}{x}$