SOLUTION: Hello, the following question is from a past exam paper on algebra & complex numbers that I am looking at in order to revise for my Calculus exam. I have the answer in front of me

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Question 167773: Hello, the following question is from a past exam paper on algebra & complex numbers that I am looking at in order to revise for my Calculus exam. I have the answer in front of me, but I do not quite understand the working behind it, so if you could clear that up for me I would be grateful.
QUESTION SIX
Solve the following equation for x in terms of q: 2^(3x-1)=7^(x-q)

The assessment schedule says that the answer should be: x=(ln2-qln7)/(3ln2-ln7) or equivalent
Found 2 solutions by jim_thompson5910, rviksub:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E%283x-1%29=7%5E%28x-q%29 Start with the given equation


ln%282%5E%283x-1%29%29=ln%287%5E%28x-q%29%29 Take the natural log of both sides. This step is needed since the variable we want to solve for is in the exponent.



%283x-1%29ln%282%29=%28x-q%29ln%287%29 Rewrite the left side using the identity ln%28x%5Ey%29=y%2Aln%28x%29%29



3x%2Aln%282%29-ln%282%29=x%2Aln%287%29-q%2Aln%287%29 Distribute


3x%2Aln%282%29-x%2Aln%287%29=-q%2Aln%287%29%2Bln%282%29 Subtract x%2Aln%287%29 from both sides. Add ln%282%29 to both sides.


3x%2Aln%282%29-x%2Aln%287%29=ln%282%29-q%2Aln%287%29 Rearrange the terms on the right side


x%283%2Aln%282%29-ln%287%29%29=ln%282%29-q%2Aln%287%29 Factor out the GCF "x" from the left side.


x=%28ln%282%29-q%2Aln%287%29%29%2F%283%2Aln%282%29-ln%287%29%29 Divide both sides by 3%2Aln%282%29-ln%287%29 to isolate "x"


So the solution is x=%28ln%282%29-q%2Aln%287%29%29%2F%283%2Aln%282%29-ln%287%29%29


Answer by rviksub(2) About Me  (Show Source):
You can put this solution on YOUR website!
2^(3x-1)=7^(x-q)
Use the property ln a^b=b ln a
Take ln on both sides,
ln 2^(3x-1)=ln 7^(x-q)
(3x-1)ln2=(x-q)ln7
3xln2-ln2=xln7-qln7
3x ln2-x ln7=ln2 -q ln7
» x(3ln2-ln7)=ln2-qln7
» x= (ln2-qln7)/(3ln2-ln7)