SOLUTION: Find the unknown in the equation using steps please:) log6 7 = log6(6^x+1 plus 6^x+2) Please note the 6 in the "log6 7" is small: Find the unknown in the equation using steps p

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Question 133440: Find the unknown in the equation using steps please:)
log6 7 = log6(6^x+1 plus 6^x+2)
Please note the 6 in the "log6 7" is small: Find the unknown in the equation using steps please:)
How can I answer this quesiton with logs appearing in at least one of the steps?
Thanks again:)
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
log6 7 = log6(6^x+1 plus 6^x+2)
It looks like (6^(x+1) + 6^(x+2)) is the inverse log on the right side.
If that is true you get:
(6^(x+1) + 6^(x+2)) = 7
---------------------
Now take the log(base 6) of both sides to get:
log6 [6^(2x+3)] = log7/log6
2x+3 = 1.08603
2x = -1.9139
x = -0.95698...
Cheers,
Stan H.

Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
the bases are the same (6) so the arguments are equal

7=6^(x+1)+6^(x+2)

6^(x+2)=(6(x+1))(6^1)=6(6^(x+1))

substituting __ 7=6^(x+1)+6(6^(x+1)) __ 7=7(6^(x+1))

dividing by 7 __ 1=6^(x+1) __ taking log __ log(1)=(x+1)log(6)

dividing by log(6) __ (log(1))/(log(6))=x+1 __ 0=x+1