SOLUTION: find x if logeX + loge3 = 1 the "e" in problem is the base. Thanks

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Question 146826This question is from textbook intermediate algebra
: find x if logeX + loge3 = 1
the "e" in problem is the base.
Thanks This question is from textbook intermediate algebra

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
When two logs of common base are added together, it is equal to the log of their product.
Therefore,
log%28e%2CX%29 + log%28e%2C3%29 = log%28e%2C3X%29
Substituting this for the left side of the given equation results in:
log%28e%2C3X%29 = 1
Now convert this equation to exponential form using the relationship:
log%28a%2CM%29 = y is equivalent to a%5Ey = M
When you apply this conversion to:
log%28e%2C3x%29 = 1
it becomes
3X = e%5E1
or just
3X = e
Solve for X by dividing both sides by 3 to get:
X =+e%2F3
Hope this helps you to understand the problem. The solution just requires you to know two rules:
(1) The rule of addition of logarithms, and
(2) The rule for converting from logarithmic form to exponential form.