log(3x+5)=2

Question

Solve the logarithmic equation for x.

Answer 1

Hello, thank you for taking the time to post your question!

The default assumption that you want to use here is that this is a base-10 logarithm. That means you can rewrite the equation as

10^2 = 3x + 5

Solving that for x then I get

100 – 5 = 3x

95 = 3x

x = 95/3

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

The log of some number is simply taking the log to the base 10 when the base number is dropped. To solve this problem just rewrite the equation in its exponential form in which is:

 

3x+5=10^2 This implies 

 

3x+5=100 Now you could use simple algebra to solve for x.