### Need help from an expert?

The world’s top online tutoring provider trusted by students, parents, and schools globally.

The solution to the equation 3^x = 81 is x = 4.

To solve this equation, we need to use logarithms. Specifically, we need to take the logarithm of both sides of the equation with respect to the base 3. This gives us:

log3(3^x) = log3(81)

Using the power rule of logarithms, we can simplify the left-hand side of the equation:

x log3(3) = log3(81)

Since log3(3) = 1, we can simplify further:

x = log3(81)

Now we need to evaluate the logarithm on the right-hand side of the equation. We can use the fact that 81 = 3^4 to rewrite the equation as:

x = log3(3^4)

Using the power rule of logarithms again, we get:

x = 4 log3(3)

Since log3(3) = 1, we can simplify further:

x = 4

Therefore, the solution to the equation 3^x = 81 is x = 4.

Study and Practice for Free

Trusted by 100,000+ Students Worldwide

Achieve Top Grades in your Exams with our Free Resources.

Practice Questions, Study Notes, and Past Exam Papers for all Subjects!

The world’s top online tutoring provider trusted by students, parents, and schools globally.

Loading...

Loading...