Question and Answers Forum

All Questions      Topic List

Logarithms Questions

Previous in All Question      Next in All Question      

Previous in Logarithms      Next in Logarithms      

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

solve: log_7 2 + log_(49) x =log_7 (√3)

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

Answered by nurtani last updated on 23/Jun/22

⇔ log_7 2+log_7 x^(1/2) =log_7 3^(1/2) ⇔ log_7 2x^(1/2) = log_7 3^(1/2) ⇔ 2x^(1/2) = 3^(1/2) ⇔ (2x^(1/2) )^2 = (3^(1/2) )^2 ⇔ 4x = 3 ⇔ x = (3/4)

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

Terms of Service

Privacy Policy

Contact: info@tinkutara.com