Question 814488: How do you figure X Log7 x+5 =12
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! I'm assuming that the equation is:
Tutor don't like having to guess what the problem is. You'll get a faster response if you express the problem clearly.
One way to make the problem clearer is to use parentheses generously. Use them to group things like function arguments, exponents, numerators, denominators, radicands, etc.
Expressing logarithms clearly can be especially difficult. Try either of the following:- Use a mix of English and math symbols. For example: One way to express the equation above would be: "(base 7 log of x) + 5 = 12", or ...
- Teach yourself algebra.com's syntax for formulas. Click on the "Show source" link above to see what I typed to get algebra.com to display the equation above. From that you can possibly learn enough to enter logarithms clearly.
If I am wrong about what the equation is, then please re-post your question. If I'm correct then keep reading...
To solve this we first isolate the logarithm. Subtracting 5 we get:
Then rewrite it in exponential form. In general  is equivalent to  . Using this pattern with our equation we get:
x = 823543
When solving these equation a check must be made. It is not optional! A solution to these equations must make all bases and arguments of all logs valid. (Valid bases are any positive number except 1 and valid arguments are any positive number.) If a "solution" makes a base or an argument invalid then it is not actually a solution and it must be rejected.
Use the original equation to check:
Checking x = 823543:
We can already see that the base, 7, and the argument, 823543, are both valid. So this solution checks out!
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