SOLUTION: I need some help with two problems. Thanks alot. Solve the logrithim equation. leave answer in exact form log x = log 2x^2 -2 solve the equation ln 4

SOLUTION: I need some help with two problems. Thanks alot. Solve the logrithim equation. leave answer in exact form log x = log 2x^2 -2 solve the equation ln 4 - ln x = 20 tha

Question 71654This question is from textbook
: I need some help with two problems. Thanks alot.
Solve the logrithim equation. leave answer in exact form
log x = log 2x^2 -2
solve the equation
ln 4 - ln x = 20

thanks again This question is from textbook

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!

.
I'm going to assume that the base of log is 10 for this problem.
.
For the time being let's just work on . I presume you know the rules
of logarithms. equals and furthermore,

.
So putting this expansion all together:
.

.
Substituting this into the original problem for the term results in:
.

.
On the right side, combining the two terms gives us:
.

.
Subtract from both sides leaves us with:
.

.
Multiply both sides by -1:
.

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Using a calculator you can find log(2) and subtract it from 2. The answer is 1.698970004.
So the equation is now:
.

.
Convert this to exponential form to find that:
.

.
The answer is that x = 50, but you can track the work and cut it off at the point
that you think satisfies the "exact form" asked for in the problem.
.
Next problem:
.

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Subtract from both sides to get:
.

.
Multiply the entire equation by -1
.

.
This time the base is .
.
Use a calculator to find ln(4) and once you get that, subtract 20. The result should be
-18.61370564. This makes the equation:
.

.
Convert this to exponential form by raising to the power -18.61370564 on your calculator.
The answer you should get is
.

.
Hope this helps you with your understanding of logarithms.
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