What you need to know

Things to remember:

  • An exponent, or power, tells us how many times we multiply a number by itself.

What is the value of x if 3^x=81?

Remember, an exponent is telling us that we multiply a number by itself a certain number of times. So, this question is asking us to see how many times we have to multiply 3 by itself to make 81. The easiest way to this is to just build it up.

x=1                     3^1=3

x=2                     3^2=3\times3=9

x=3                     3^3=3\times3\times3=9\times3=27

x=4                     3^4=3\times3\times3\times3=9\times3\times=27\times3=81

So, we can see that x=4!

3^4=81

Example Questions

Question 1: What is the value of x if 4^x=16?

Answer

x=1                     4^1=4

 

x=2                     4^2=4\times4=16

 

So, we can see that x=4!

 

4^2=16

Question 2: What is the value of x if 5^x=625?

Answer

x=1                     5^1=4

x=2                     5^2=5\times5=25

 

x=3                     5^3=5\times5\times5=25\times5=125

 

x=45^4=5\times5\times5\times5=25\times5\times5=125\times5=625

 

So, we can see that x=4!

 

5^4=625