Math exercise

Question

Solve for x: log(3x+5)=2.

Answer 1

First, use the base of the log to undo the log. (Here the base of the log is 10 since no subscript comes after the log.) 

 

Our first step looks like:

 

                                                                      10^log(3x+5) = 10² 

 

Compare this with the original equation. How do we get 10²?

 

Second, the left side of the above equation CANCELS to 3x+5 (this is why we did the first step), and the right side become 100. So, our second step looks like:

 

                                                                              3x+5 = 100

 

Third, subtracting by 5 and dividing by 3 we get:

 

                                                                                    x = 95/3 ~ 31.667

 

Fourth, pat yourself on the back. Now, you can solve log equations!

 

Note: If the base of the log is not something than 10, say 4 instead, our first step would look like:

 

                                                                              4^3x+5 = 4² 

 

We could continue in a similar fashion to what we did above.

 

-20pi

Answer 2

log(3x+5) = 2

 

Convert to exponential form to get:  3x+5 = 10²

 

                                                                3x + 5 = 100

 

                                                                      3x = 95

 

                                                                        x = 95/3