If 2-3x-2-3-22-2x - then x

Finding the value for x:(2/3)^x+2=(3/2)^2 2x (3/2)^ x 2=(3/2)^2 2x Compare powers on both sides [ x 2 =2 2x; x =4 ]Hence, the value of x is 4. ...

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Byju's Answer

Standard XII

Mathematics

Monotonically Increasing Functions

If 2/3x+2=3/2...

Question

If ${(\frac{2}{3})}^{x + 2} = {(\frac{3}{2})}^{2 - 2 x}$ , then $x$

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Solution

Finding the value for $x$ :
${(\frac{2}{3})}^{x + 2} = {(\frac{3}{2})}^{2 - 2 x}$
${(\frac{3}{2})}^{- x - 2} = {(\frac{3}{2})}^{2 - 2 x}$
Compare powers on both sides
$\begin{aligned} - x - 2 & = 2 - 2 x \\ x & = 4 \end{aligned}$
Hence, the value of $x$ is $4$ .

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