Final answer:
To solve the exponential equation 4+3⁵ˣ=8, subtract 4 from both sides and take the logarithm of both sides. Divide both sides by log(3) to solve for x, which is approximately 0.6697.
Step-by-step explanation:
To solve the exponential equation 4+3⁵ˣ=8, we need to isolate the variable x. We can do this by subtracting 4 from both sides of the equation:
3⁵ˣ = 8 - 4
3⁵ˣ = 4
Next, we can take the logarithm of both sides of the equation to eliminate the exponent:
log(3⁵ˣ) = log(4)
Using the property of logarithms, we can bring down the exponent:
5ˣ * log(3) = log(4)
Finally, we can divide both sides of the equation by log(3) to solve for x:
5ˣ = log(4) / log(3)
x = log(4) / log(3 * 5)
Using a calculator, we can find the value of x to be approximately 0.6697.