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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

J. W. Tanner
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Glenn Boll
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  • Welcome to Mathematics Stack Exchange. Use rules like $\log a - \log b = \log (a/b)$, $\log a + \log b=\log (a\cdot b),$ and $\log (a^n)=n \log a$ – J. W. Tanner Sep 06 '19 at 19:12
  • @J.W.Tanner Thanks for the welcome, I was able to solve the first few steps but I was stuck, your answer below helped me solve it, thanks. – Glenn Boll Sep 06 '19 at 19:15

2 Answers2

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Hints:

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

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

J. W. Tanner
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$$\log_2 x - \log_2 5 = 2 + \log_2 3$$

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}

Bernard
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user1952500
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