Solve 1.5^x = 70. Round your answer to the nearest hundredth.
1.5^x = 70
x ln1.5 = ln70
x = ln(70)/ln(1.5)
To solve the equation 1.5^x = 70, we need to isolate the variable x. Here's how you can find the solution:
Step 1: Take the logarithm of both sides of the equation. The choice of logarithm base is up to you, but commonly used bases are 10 (log) and natural logarithm (ln) with base e. Let's choose the natural logarithm (ln) for this case.
ln(1.5^x) = ln(70)
Step 2: Apply the logarithmic rule for exponentials:
x * ln(1.5) = ln(70)
Step 3: Solve for x by dividing both sides of the equation by ln(1.5):
x = ln(70) / ln(1.5)
Step 4: Use a calculator to evaluate the right side of the equation:
x ≈ 4.804
Step 5: Round the answer to the nearest hundredth:
x ≈ 4.80
Therefore, the solution to the equation 1.5^x = 70, rounded to the nearest hundredth, is x ≈ 4.80.