Question 678813
First of all, is the equation
{{{10^(3x+1) = 100}}}
or
{{{10^3x+1 = 100}}}?
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.<br>
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.<br>
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:
{{{10^(3x+1) = 10^2}}}<br>
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