SOLUTION: Solve the exponential or logarithmic equations. (Write your final answer in BOTH exact and approximate value).
(a) 6^x-3 = 2^x
(b) log(5x-6) = 2log x
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Question 149398: Solve the exponential or logarithmic equations. (Write your final answer in BOTH exact and approximate value).
(a) 6^x-3 = 2^x
(b) log(5x-6) = 2log x
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(a) 6^x-3 = 2^x
Take the log of both sides to get:
(x-3)log6 = xlog2
x(log6-log2) = 3log6
x(log3) = 3log6
x = 3log6/log3
x = 4.8927...
-------------------------
(b) log(5x-6) = 2log x
log(5x-6) = logx^2
x^2 = 5x-6
x^2-5x+6=0
(x-3)(x-2) = 0
x = 2 or x = 3
----------------------
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you started.
a)
Start with the given equation.
Take the log of both sides.
Rewrite both sides using the identity
Distribute.
Subtract from both sides.
Add to both sides.
Factor out the GCF "x"
Combine the logs using the identity
Divide.
Divide both sides by to isolate x
Rewrite the expression using the identity
Raise 6 to the 3rd power to get 216
Use the change of base formula to rewrite the right side.
So the exact answer is which approximates to
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