SOLUTION: I am having a hard time learning logarithm.
Solve the equation. Give an exact solution.
4^(x+6) = 7
Algebra.Com
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) (Show Source): You can put this solution on YOUR website!
Given:
.
.
Solve for x
.
Take the log base 10 of both sides and you get:
.
.
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:
.
.
Divide both sides of the equation by log(4). When you do, the resulting equation is:
.
.
Next subtract 6 from both sides of the equation to get:
.
.
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:
.
.
The division results in the equation becoming:
.
.
Hope this helps you understand the problem and how to use logarithms to solve it.
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