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Question Number 171990 by Mikenice last updated on 22/Jun/22

$$solve:$$$${log}_{7}2+{log}_{49}x={log}_7\sqrt{3}$$

Answered by nurtani last updated on 23/Jun/22

$$\iff {log}_{7}2+{log}_7{x}^{\frac{1}{2}}={log}_7{3}^{\frac{1}{2}}$$$$\iff {log}_{7}2x^{\frac{1}{2}}={log}_7{3}^{\frac{1}{2}}$$$$\iff 2x^{\frac{1}{2}}=3^{\frac{1}{2}}$$$$\iff {\left(2x^{\frac{1}{2}}\right)}^2={\left(3^{\frac{1}{2}}\right)}^2$$$$\iff 4x=3$$$$\iff x=\frac{3}{4}$$

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