SOLUTION: I was absent and my friend got my homework for me. My homework is not from the textbook and I missed the instruction. Would someone please work this problem in easy to follow steps

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I was absent and my friend got my homework for me. My homework is not from the textbook and I missed the instruction. Would someone please work this problem in easy to follow steps      Log On


   

Question 127650: I was absent and my friend got my homework for me. My homework is not from the textbook and I missed the instruction. Would someone please work this problem in easy to follow steps so I can figure out how to complete the rest of my assignment? PLEASE ?
7^(2x+3)=5^(x-4)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
7^(2x+3) = 5^(x-4)
:
Use natural logs to solve this:
ln%287%5E%282x%2B3%29%29+=+ln%285%5E%28x-4%29%29
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Using the log equivalent of exponents, we can write it:
%282x%2B3%29%2Aln%287%29+=+%28x-4%29%2Aln%285%29
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Find nat log (ln) of 7 and 5:
1.9459(2x+3) = 1.6094(x-4)
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Multiply what's inside the brackets
3.8918x + 5.8377 = 1.6094x - 6.4376
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Some basic algebra
3.8918x - 1.6094x = -6.4376 - 5.8377
:
2.2824x = -12.2753
x = %28-12.2753%29%2F2.2824
x = -5.378
:
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Check solution on a good calc:
enter 7^(2(-5.378)+3) = 2.7888
enter 5^(-5.378-4) = 2.7865, close enough to check our solution
;
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Did this make sense? You can use common logs (base 10) if you prefer, the method is the same. (the numbers will be different, but the answer will be the same)