Solving a logarithim, log81 (x) = 3/4

The video tutorial explains how to solve for X using logarithms. It begins with an introduction to the concept of logarithms, using the example of log base three of 9 equals 2, and explains how this relates to exponents. The tutorial then demonstrates solving the expression 81 to the 3/4 power by rewriting it in terms of exponents and using the power rule. The process involves rewriting 81 as 3 to the 4th power and applying the power of a power rule to find that X equals 27.

What does log base 3 of 9 equal, and why?

• 1, because 3 raised to the power of 1 equals 9

• 2, because 3 raised to the power of 2 equals 9

• 4, because 3 raised to the power of 4 equals 9

• 3, because 3 raised to the power of 3 equals 9

How can you express 81 to the 3/4 power using roots?

• As the cube root of 81 to the fourth power

• As the square root of 81 to the third power

• As the fifth root of 81 to the second power

• As the fourth root of 81 to the third power

If you don't have a calculator, how can you simplify 81 to the 3/4 power?

• Rewrite 81 as 3 to the 4th power and multiply by 3/4

• Rewrite 81 as 9 squared and multiply by 3/4

• Rewrite 81 as 27 to the 1.5 power

• Rewrite 81 as 3 to the 3rd power and multiply by 4/3

What is the result of 3 raised to the power of 3?

• 9

• 18

• 27

• 81

Why is it useful to express 81 as 3 to the 4th power when solving for X?

• It reduces the need for a calculator by simplifying to a single digit

• It makes the calculation easier by converting it to a base 10 problem

• It allows the use of the power rule of exponents to simplify the expression

• It helps in visualizing the problem as a geometric sequence