- #1

Yankel

- 395

- 0

I need assistance in solving this exponential equation.

\[54\cdot 2^{2x}=72^{x}\cdot \sqrt{0.5}\]

The final answer should be 3/2.

My strategy was to try and bring to a state where the exponents are equal. We know that 54 is 6 times 9. We also know 72 is 8 times 9. The solution probably involves the fact that 9 appears in both numbers.

Can you kindly assist ? Oh, one more thing, important thing. The use of logarithms is forbidden... :-)

Thank you .