Solve for \( x \) in the equation:
\[
\log_{\frac{2}{3}} \frac{9}{4} = x + 3
\]
Answer (3)
l o g 3 2 4 9 = x + 3 l o g 3 2 ( 3 2 ) − 2 = x + 3 − 2 = x + 3 − x = 3 + 2 − x = 5 / \cdor ( − 1 ) x = − 5
l o g 3 2 4 9 = x 3 ( 3 2 ) x + 3 = 4 9 ( 3 2 ) x + 3 = ( 3 2 ) − 2 x + 3 = − 2 x = − 2 − 3 x = − 5
To solve lo g 3 2 4 9 = x + 3 , first isolate x and compute lo g 3 2 4 9 using the change of base formula. After simplifying using logarithmic identities, you will find x ≈ − 5 .
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