Get the answers you've been searching for with IDNLearn.com. Receive prompt and accurate responses to your questions from our community of knowledgeable professionals ready to assist you at any time.
Given:
The equation is
[tex]\left(\dfrac{3}{5}\right)^x\left(\dfrac{5}{3}\right)^{2x}=\dfrac{125}{27}[/tex]
To find:
The value of x.
Solution:
We have,
[tex]\left(\dfrac{3}{5}\right)^x\left(\dfrac{5}{3}\right)^{2x}=\dfrac{125}{27}[/tex]
[tex]\left(\dfrac{5}{3}\right)^{-x}\left(\dfrac{5}{3}\right)^{2x}=\dfrac{5\times 5\times 5}{3\times 3\times 3}[/tex] [tex][\because \left(\dfrac{a}{b}\right)^{-m}=\left(\dfrac{b}{a}\right)^{m}][/tex]
[tex]\left(\dfrac{5}{3}\right)^{-x+2x}=\dfrac{5^3}{3^3}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]\left(\dfrac{5}{3}\right)^{x}=\left(\dfrac{5}{3}\right)^{3}[/tex]
On comparing the exponents, we get
[tex]x=3[/tex]
Therefore, the value of x is 3.