Final answer:
To solve the equation 3^x/4 = 9 for x, we can isolate the variable by multiplying both sides by 4 and then take the logarithm of both sides. Using the change of base formula, we can evaluate log(36) / log(3) to find the approximate value of x rounded to the nearest hundredth.
Step-by-step explanation:
To solve for x in the equation 3^x/4 = 9, we can start by isolating the variable x. First, we can multiply both sides of the equation by 4 to get rid of the fraction: 3^x = 9 * 4. Next, we can rewrite 9 * 4 as 36. So the equation becomes 3^x = 36. To solve for x, we can take the logarithm of both sides of the equation. We choose the logarithm base that will help remove the exponent. In this case, using the logarithm base 3 will cancel out the exponent on the left side. Taking the logarithm base 3 of both sides gives us x = log3(36). Using the change of base formula, we can rewrite log3(36) as log(36) / log(3). Using a calculator, we can evaluate this expression and round to the nearest hundredth to find the approximate value of x.
Learn more about Solving Exponential Equations