Solve the equation. (\frac{2}{3})^{x}=\frac{9}{4}

Ernstfalld

Ernstfalld

Answered question

2021-09-28

Solve the equation. (23)x=94

Answer & Explanation

Fatema Sutton

Fatema Sutton

Skilled2021-09-29Added 88 answers

Step 1
We have to solve the equation:
(23)x=94
Rewriting the equation,
(23)x=94
(23)x=3×32×2
(23)x=3222
(23)x=(32)2
We know the exponents rule,
(ab)m=(ba)m
am=bnm=n
Step 2
Therefore,
(23)x=(32)2
(23)x=(23)2
Comparing the exponent,
x=−2
Hence, solution of the equation is x=−2.

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