SOLUTION: log_x 100 = 1/2
log_x1024 = 10
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Question 238089: log_x 100 = 1/2
log_x1024 = 10
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
For problems like yours, where the variable is the base or in the argument of the logarithm, the key is to rewrite the logarithmic equation in exponential form. To do this we need to know that is equivalent to .
Rewriting this in exponential form we get:
The equation is now solvable. We just square both sides:
which simplifies to
Rewriting this in exponential form we get:
If you are a computer geek you may recognize that . Otherwise we find the 10th root of each side:
The left side is the same as which we can find using a calculator. The right side simplifies to . So now we have:
Solving this we get
or
And, since x is the base of a logarithm, we must reject x = -2. So the only solution is x = 2.
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