solve: x^3.5=41.15
take log of each side
3.5 log x=log41.15
logx=log(41.15)/ (3.5)= .4612
x= 10^.4612=2.892
To solve the equation x^3.5 = 41.15, we can use logarithms to isolate x.
Step 1: Take the logarithm of both sides of the equation. Since the exponent is 3.5, we can use the natural logarithm (ln) or logarithm base 10 (log).
ln(x^3.5) = ln(41.15)
Step 2: Apply the logarithm rules to bring down the exponent:
3.5 * ln(x) = ln(41.15)
Step 3: Divide both sides of the equation by 3.5:
ln(x) = ln(41.15) / 3.5
Step 4: Use the inverse function of the natural logarithm to cancel it out. In this case, it is the exponential function (e^x):
x = e^(ln(41.15) / 3.5)
Step 5: Evaluate the expression using a calculator:
x ≈ 2.970
Therefore, the approximate value of x that satisfies the equation x^3.5 = 41.15 is x ≈ 2.970.