Question 985584: Given x > 1, solve for x
(log x^7)(log x) − log x^2 − 5 = 0
I had x = 10
and received the following feedback:
Note that in mathematics, log with no base is loge which is often also written as ln. Your answer should therefore be in terms of e (not 10).
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! No. Unstated base is either understood through context, or commonly taken as base 10, or understood by convention according to the typical practices for a field or work or study, base e or base 10. The base to be understood in your class needs to be instructed to you before you/or while you are starting your studies of logarithms.
ln, will mean logarithm to the base of the natural logarithm, e, the number being APPROXIMATELY 2.71828...., an irrational number. If the expectation is logarithm is to base e, then this should be ln(). Otherwise, unstated logarithm base should be assumed common log, base ten.
You want to know the convention in your class before you begin most of your logarithm studies.
Looking into your equation, it is essentially quadratic form:
from which you find
 OR  .
Use the base that you need, and find your corresponding x.
If base e, then either x=0.4895 or x=2.71828, or e.
I see NO justification for x>1; maybe another tutor will do this differently.
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