Final answer:
To solve the equation f(x) = g(x), you can set the two functions equal to each other and solve for x using logarithms. The solution to f(x) = g(x) is approximately 0.457.
Step-by-step explanation:
To solve the equation f(x) = g(x), we need to set the two functions equal to each other and solve for x. So, we have:
7(2.6)^x = 55(1.5)^x
To solve this type of equation, we can take the logarithm of both sides. Let's take the natural logarithm (ln) of both sides:
ln(7(2.6)^x) = ln(55(1.5)^x)
Using the properties of logarithms, we can simplify the equation:
x(ln(7) + ln(2.6)) = x(ln(55) + ln(1.5))
Now, divide both sides by (ln(7) + ln(2.6)):
x = (ln(55) + ln(1.5)) / (ln(7) + ln(2.6))
Using a calculator to evaluate the right side of the equation, we find:
x ≈ 0.457