To solve the equation 5^x = 2^(x + 3), we can take the logarithm of both sides and use logarithm properties to simplify:
xlog(5) = (x + 3)log(2)
Expanding the equation:
xlog(5) = xlog(2) + 3log(2)
Rearranging terms:
xlog(5) - xlog(2) = 3log(2)
Factoring out x:
x(log(5) - log(2)) = 3log(2)
Simplifying the logarithmic terms using log properties:
x(log(5/2)) = 3log(2)
Dividing both sides by (log(5/2)):
x = 3log(2) / log(5/2)
Using a calculator and evaluating to 4 significant figures:
x ≈ 6.767
Solve giving your answer to 4 s.f
5^x = 2^(x + 3)
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1 answer