How to answer a logarithm question

Question

Can anyone please show me how to solve this question step by step? $x$ should equal 60. $$\log_2 x - \log_2 5 = 2 + \log_2 3$$

Thanks in advance

Answer 1

Hints:

$$\log_2x-\log_2 5=\log_2 (x/5)$$

$$2+\log_2 3=\log_2 4+\log_2 3=\log_2 12$$

Answer 2

$$\log_2 x - \log_2 5 = 2 + \log_2 3$$

Using both sides as a power of $2$, \begin{align}&2^{\log_2 x - \log_2 5} = 2^{2 + \log_2 3}\\ \implies &\frac{2^{\log_2 x}}{2^{\log_2 5}} = 2^2 \cdot 2^{\log_2 3}\\[1ex] \implies &\frac{x}{5} = 4\cdot 3 \\ \implies& x = 60 \end{align}