SOLUTION: Hello, I am working a test review sheet for a test coming up but I have a problem that I am not sure how to work out and I can't find a similar example in my notes or text book. I

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello, I am working a test review sheet for a test coming up but I have a problem that I am not sure how to work out and I can't find a similar example in my notes or text book. I       Log On


   

Question 365947: Hello, I am working a test review sheet for a test coming up but I have a problem that I am not sure how to work out and I can't find a similar example in my notes or text book. I simply need to solve the equation below.
5(1.044)^x = x+10
This problem is throwing me off because the x on the left is an exponent and the x on the right is not, so I am unsure how to combine them.
x log(1.044) = log((x+10)/5) ...seems WORSE!!
Also, I tried using the graphing calculator method to find the value of x by graphing and calculating the intersection of these two equations. My answer was x = -6.17. Is this the proper time to use that method or am I just completely wrong? If it IS a negative number than it cannot be a logarithm right?
Thanks in advance!

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is throwing me off because the x on the left is an exponent and the x on the right is not, so I am unsure how to combine them.
x log(1.044) = log((x+10)/5) ...seems WORSE!!
Also, I tried using the graphing calculator method to find the value of x by graphing and calculating the intersection of these two equations. My answer was x = -6.17. Is this the proper time to use that method or am I just completely wrong? If it IS a negative number than it cannot be a logarithm right?
:
I have often resorted to the graphing calc, in these types of problems:
A single equation: y = 5(1.044)^x - (x+10) will produce a graph:
+graph%28+300%2C+200%2C+-8%2C+4%2C+-10%2C+10%2C+5%281.044%29%5Ex-%28x%2B10%29%29+
x intercept = -6.066; which checks out in the original equation
:
A log equiv equation will produce the same intercept on my Ti83
y+=+x+-+%28log%28%28.2x%2B2%29%29%29%2F%28log%28%281.044%29%29%29
Although I can't seem do this on this graphing feature here.
:
You cannot have a log of negative number, but you can have a log of a number with a negative exponent.
:
:
Are you allowed to use a graphing calc to solve these kind of problems?
If not I guess this is not much help. Perhaps you can resubmit and see
if one of the real smart guys on this forum will help.