SOLUTION: I understand the concepts behind natural logarithms and solving for an exponent, but on this test review, there are problems for which I was not prepared by either my text or the h

Question 769968: I understand the concepts behind natural logarithms and solving for an exponent, but on this test review, there are problems for which I was not prepared by either my text or the homework. Here is an example:
x^2-6x+4=e^(x-7)+3
We are meant to use the calculator and solve for x as an approximate decimal. I am baffled as to what to do once I have gotten to
ln(x^2-6x+1)=(x-7)ln(e)
How do I solve for x when (x-7) is alone, (having been multiplied by ln(e), which is one)but the quadratic is still in ln form?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
x^2-6x+4=e^(x-7)+3
We are meant to use the calculator and solve for x as an approximate decimal. I am baffled as to what to do once I have gotten to
ln(x^2-6x+1)=(x-7)ln(e)
How do I solve for x when (x-7) is alone, (having been multiplied by ln(e), which is one)but the quadratic is still in ln form?
----------------
ln(e) = 1, so you can eliminate that.
-----
ln(x^2-6x+1)=(x-7)
That doesn't help a lot. The only method here is graphical or numerical.
------
x =~ 0.1713815470435187
x =~ 5.885861739266182
x =~ 11.0354521340621
================

RELATED QUESTIONS
Ok so i'm studying for a math test and it's about logarithms and on the review it has a... (answered by solver91311)

Without using a calculator how do you solve 5^(123/1000)? I know this problem can be... (answered by josgarithmetic)

Find the age of me "in 12 years i will be three times as old as i was 32 years ago"... (answered by josgarithmetic)

A jar contains 24 red and blue marbles. If the probability of selecting a red marble at... (answered by DrBeeee)

My problem is log3x=5, im not sure what this is called but the "3" is the opposite of an... (answered by user_dude2008)

I don't understand the... (answered by stanbon)

Hi- I teach Adult Basic Education, mostly I help students pass the GED test. I am no... (answered by Fombitz,stanbon)

Hi, I'm studying for a test and the problem below seems so simple, but I can't figure... (answered by scott8148)

I am lost on this one. Is there anyone that help me out? Thanks Assume that x, y, z... (answered by stanbon)