SOLUTION: ln(5x-2)=2

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Question 1149546: ln(5x-2)=2
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

To isolate x, we need to use the rule that if y+=+ln%28x%29, then e%5Ey+=+x

So,

ln%285x-2%29+=+2 starting equation

5x-2+=+e%5E2 use the rule mentioned above

5x+=+e%5E2%2B2 add 2 to both sides

x+=+%28e%5E2%2B2%29%2F5 divide both sides by 5

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Extra info:
The letter 'e' represents the constant 2.71828182846
It is similar to how pi = 3.1415926535898
Both values have no pattern to the digits and the decimal digits go on forever, which makes those decimal representations to be approximations.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Remember the basic definition of a logarithm: "The logarithm of a number (5x-2) is the power (2) to which the base (e) must be raised to equal the number", so we can express this as:
ln%285x-2%29+=+2 ---> e%5E2+=+%285x-2%29
Now we can solve for x.
e%5E2+=+5x-2.......... Add 2 to both sides.
e%5E2%2B2+=+5x......... Divide both sides by 5.
x=%281%2F5%29+%28e%5E2%2B2%29->exact answer
which
x+=+1.8778 ->approximately.