Question

Tisk the value of x if 6/5x 5/6²x = 125/216

HELP ME ​

Answer 1

Answer:

The value of x is 3 in \bold{\left(\frac{6}{5}\right)^{x} \times\left(\frac{5}{6}\right)^{2 x}=\frac{125}{216}}(56)x×(65)2x=216125

Solution:

The power of the \frac{6}{5} \& \frac{5}{6}56&65  can be equated to find out the term x  

Now to find the term x we need to equal both the terms like changing \frac{6}{5} t o \frac{5}{6}56to65 so that we can easily equate the equation.

\begin{gathered}\begin{array}{l}{\left(\frac{6}{5}\right)^{x} \times\left(\frac{5}{6}\right)^{2 x}=\frac{125}{216}} \\ \\{\left(\frac{5}{6}\right)^{-x} \times\left(\frac{5}{6}\right)^{2 x}=\frac{125}{216}}\end{array}\end{gathered}(56)x×(65)2x=216125(65)−x×(65)2x=216125

Taking 5/6 common, we get  

\left(\frac{5}{6}\right)^{-x+2 x}=\frac{125}{216}=\left[\frac{5}{6}\right]^{3}(65)−x+2x=216125=[65]3

Placing 125 and 215 as respective cube of 5 and 6 we get ,

\left(\frac{5}{6}\right)^{-x+2 x}=\left[\frac{5}{6}\right]^{3}(65)−x+2x=[65]3

As we can see the identity is same, we can equate the powers, after equating the powers we get

-x + 2x = 3

x = 3

Answer 2

Step-by-step explanation:

x12/23/568/124/520/43