SOLUTION: 10^3x+1=100 what does x equal? x= ?

Question 678813: 10^3x+1=100 what does x equal?
x= ?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
First of all, is the equation

or
?
I think you meant the first one but what you entered meant the second one. If I'm right then please put parentheses around multiple-term exponents. If I'm wrong then the rest of this will not help because I will be solving the first one.

Solving equations where the variable is in an exponent can be done with logarithms. However there is an easier solution if the equation can be rewritten so each side is a power of the same number. Your equation can be solved this way.

The left side is already a power of 10. Can we rewrite the right side so that it is also a power of 10? Or can we rewrite both sides so that they are both powers of the same third number? The answer to the first question is yes:

The equation now says that two powers of 10 are equal. The only way this can be true is if the exponents are equal. So:
3x+1 = 2
This is simple to solve:
3x = 1
x = 1/3
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