Hire a tutor

Solve the equation 3^x = 81.

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!

Need help from an expert?

4.92/5 based on480 reviews

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

Related Maths a-level Answers

    Read All Answers
    Loading...