Final answer:
The solution to the equation log 3(x) = 8 is found by converting the logarithmic equation to its exponential form, which gives us 3^8 = x. Calculating 3 raised to the power of 8, we find that x equals 6561.
Step-by-step explanation:
The solution to the equation log 3(x) = 8 can be found by understanding the properties of logarithms. According to the property of logarithms that states the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number, we can rewrite the equation in its exponential form.
Using the base of the logarithm, which is 3 in this case, the equation becomes 38 = x. Therefore, we simply need to calculate 3 raised to the power of 8 to find the value of x. This calculation results in x = 38 = 6561.
The step-by-step explanation is:
- Identify the base of the logarithm, which is 3.
- Rewrite the logarithmic equation in exponential form: 38 = x.
- Calculate 3 raised to the power of 8 to find the value of x.
- The solution to the equation is x = 6561.