You can put this solution on YOUR website!
Your equation makes no sense. The parentheses are not even balanced. So I cannot help you with it.
But here are some general tips:
- Isolate the base and its exponent with a variable.
- Find the logarithm of each side of the equation. Generally the base you use does not matter. If you want a decimal approximation of the answer, use a base for the logarithms which your calculator "knows" (like base 10 or base e (ln)). Sometimes it is helpful to choose the base of the logarithm to match the base on which there is an exponent with the variable.After steps #1 and #2, you should have an equation where one side is the log of a number with an exponent that has the variable for which you're trying to solve. On this logarithm, use the property of logarithms, , to move the exponent in the argument out in front. This is how you get a variable out of an exponent.
- Solve the resulting equation for the variable.
Here's an example:
1. Isolate the base and its exponent. Add 7 to both sides:
Divide both sides of the equation by 3:
2. Find the log of each side. If we want a simple, exact answer, use base 4 logarithms. If we want a decimal approximation, use base 10 or base e logarithms. I will base 4. (At the end I will use base 10 logarithms so you can see that, too.)
3. Use the property of logarithms to move the exponent out in front:
(which is why I chose base 4 logarithms) this becomes:
4. Solve the equation. All we need to do is add 3 to each side:
This is an exact answer to the example problem.
At step #2, if we use base 10 logarithms instead, we get:
Then, using the property of logarithms we get:
And to solve for x we divide both sides by log(4):
and add 3 to each side:
This is also an exact answer to the example equation. And if we use our calculators we can find a decimal approximation of the answer: