Question

Solve each equation for x. Convert to an exponential equation. Simplify and solve the equation to find the solution.
5=log_3(x^2+18)
2=log(3x+4)

Answer 1

For number 1, We can raise each side to the power 3

\[\large 5 = log_3(x^2 + 18)\]
\[\large 3^5 = 3^{log_3(x^2 + 18)}\]

Now remember that \(\large 3^{(log_3(x))} = x\)

so we have

\[\large 3^5 = x^2 + 18\]
\[\large 243 = x^2 + 18\]
\[\large x^2 = 225\]
\[\large x = \pm 15\]

Did that make sense?

Answer 2

Yeah thank you!

Answer 3

No problem, and you can use basically the same thing for question 2, however if there is no base of the log, we use the power 10

Answer 4

Kkay and for the first one 3^(log_3(x)) = x is the exponential equation right

Answer 5

Well THAT is a way of simplifying logarithms.

The actual exponential equation came from that

\[\large 3^5 = 3^{log_3(x^2 + 18)}\]

Answer 6

Ohh alright thanks

Answer 7

could you help me on another one? I'm about to post it..

Answer 8

Sure :)