Question

Which graph would help solve the equation5log(x+3)=5?

Answer 1

Method 1:
By graphing, we can find the graph of y = 5log(x + 3) and y = 5 to see where they intersect.

Method 2:
Alternatively, by subtracting 5 from both sides, we can find where the graph 5log(x + 3) - 5 hits the x-axis. In essence, we are finding when y hits 0 and thus, finding where it hits the x-axis.

Method 3:
We can also just solve this algebraically. When we don't have any superscripts, we take the assumption that we're working in base 10.

Divide both sides by 5:
$log(x + 3) = 1$

Take the inverse of log(x + 3) to both sides:
$10^{log_{10}(x + 3)} = 10^{1}$
$x + 3 = 10$
$x = 7$

Hence, we know that at x = 7, 5log(7 + 3) = 5.

The graphs of Method 1 is pictured first, and the graph of Method 2 is pictured on the right.