Question 20

If $$\log_{25}\left[5 \log_3 (1 + \log_3(1 + 2 \log_2 x))\right] = \frac{1}{2}$$ then x is:

Solution

$$\log_{25}\left[5 \log_3 (1 + \log_3(1 + 2 \log_2 x))\right] = \dfrac{1}{2}$$

$$\left[5\log_3(1+\log_3(1+2\log_2x))\right]=(25)^{\frac{1}{2}}$$

$$\left[5\log_3(1+\log_3(1+2\log_2x))\right]=5$$

$$\log_3(1+\log_3(1+2\log_2x))=1$$

$$1+\log_3(1+2\log_2x)=3$$

$$\log_3(1+2\log_2x)=2$$

$$(1+2\log_2x)=9$$

$$2\log_2x=8$$

$$\log_2x=4$$

$$x=16$$

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