You can
put this solution on YOUR website!Evaluate:
.
.
By the rules of logarithms, when you have the difference of two logarithms (same base) it
is equivalent to the division of the two quantities with the negative logarithm being the
denominator. Applying that rule to this problem, converts the problem to:
.
.
Next you can convert this logarithmic form to exponential form by using the translation that:
.
is equivalent to the exponential form
.
In this problem
,
, and
.
In exponential form your problem becomes:
.
.
or by transposing and converting 10^1 to just 10:
.
.
Get rid of the denominator by multiplying both sides by (x-1) to get:
.
.
Subtracting 10x from both sides results in:
.
.
Then subtracting 3 from both sides simplifies the equation to:
.
.
Finally, solve for x by dividing both sides by -9:
.
.
Check by substituting this value for x into the original problem:
.
.
Simplify the terms that the log function is operating on:
.
.
Using a calculator, you can determine that
and
.
Substituting these values results in:
.
.
and if you combine the two values on the left side you get approximately that:
.
1 = 1
.
So within round-off error, the answer that x = 1.4444444... is correct. Hope this helps
you to understand the problem. Cheers!
.
(