KnowledgeBoat Logo
|

Mathematics

Solve for x, if :

logx 49 - logx 7 + logx 1343\dfrac{1}{343} + 2 = 0

Logarithms

6 Likes

Answer

Given,

⇒logx 49+logx 1343−logx7=−2⇒logx 49×13437=−2⇒logx 497×343=−2⇒logx 149=−2⇒x−2=149⇒x−2=172⇒x−2=7−2⇒x=7.\Rightarrow \text{log}x \space {49} + \text{log}x \space {\dfrac{1}{343}} - \text{log}x7 = -2 \\[1em] \Rightarrow \text{log}x \space {\dfrac{49 \times \dfrac{1}{343}}{7}} = -2 \\[1em] \Rightarrow \text{log}x \space {\dfrac{49}{7 \times 343}} = -2 \\[1em] \Rightarrow \text{log}x \space {\dfrac{1}{49}} = -2 \\[1em] \Rightarrow x^{-2} = \dfrac{1}{49} \\[1em] \Rightarrow x^{-2} = \dfrac{1}{7^2} \\[1em] \Rightarrow x^{-2} = 7^{-2} \\[1em] \Rightarrow x = 7.

Hence, x = 7.

Answered By

2 Likes

Related Questions