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Solve for x. 5²ˣ = 17 What is the solution? x = ___ (Round to two decimal places as needed. Use a comma to separate answers as needed.)

User Ryan Burn
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Final answer:

To solve the equation 5²ˣ = 17, we can take the logarithm base 5 of both sides to isolate x. The approximate value of x is 1.27096.

Step-by-step explanation:

To solve the equation 5^2x = 17, we need to isolate x. To do that, we can take the logarithm of both sides of the equation. Since the base is 5, we can take the logarithm base 5 of both sides.

log_5(5^2x) = log_5(17)

2x = log_5(17)

x = log_5(17)/2

Using a calculator, we can find the approximate value of x to be 1.27096.

In mathematics, the logarithm is the inverse function to exponentiation. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x

Learn more about Solving exponential equations

User Diegoperini
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