SOLUTION: I am having a hard time learning logarithm. Solve the equation. Give an exact solution. 4^(x+6) = 7

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Question 85348: I am having a hard time learning logarithm.
Solve the equation. Give an exact solution.
4^(x+6) = 7
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
4%5E%28x%2B6%29+=+7
.
Solve for x
.
Take the log base 10 of both sides and you get:
.
log%28%284%5E%28x%2B6%29%29%29+=+log%28%287%29%29
.
One of the rules of logarithms is that if you have the logarithm of a quantity that is
raised to an exponent, it is equivalent to the exponent times the logarithm of just the
quantity.
.
In this problem that translates to multiplying the exponent of (x + 6) times the logarithm of 4.
This makes the equation become:
.
%28x%2B6%29%2Alog%28%284%29%29+=+log%28%287%29%29
.
Divide both sides of the equation by log(4). When you do, the resulting equation is:
.
%28x%2B6%29+=+%28log%28%287%29%29%2Flog%28%284%29%29%29
.
Next subtract 6 from both sides of the equation to get:
.
x+=+-6+%2B+%28log%28%287%29%29%2Flog%28%284%29%29%29
.
This is the basic answer. You can convert this to decimals by using a calculator to determine
the values of log(7) and log(4). When you do that you get that log(7) = 0.84509804 and
log(4) = 0.602059991. Substituting these results in:
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x+=+-+6+%2B%280.84509804%2F0.602059991%29
.
The division results in the equation becoming:
.
+x+=+-6+%2B+1.403677461+=+-4.596322539
.
Hope this helps you understand the problem and how to use logarithms to solve it.