You can put this solution on YOUR website!
Solving equations like this, with the variable in the argument of a logarithm, usually starts with using algebra and/or properties of logarithms to transform the equation into one of the following forms:
log(expression) = other-expression
or
log(expression) = log(other-expression)
If we can find a way to combine the two logarithms on the left side of your equation, then we would have the second form. They are not like terms so we cannot just add them together. (Like logarithmic terms have the same bases and the same arguments.) But there is a property of logarithms, , which gives us another way to combine two logas that have a "+" between them. (This property requires the same bases and coefficients of 1. Your logs meet both of these requirements.) Using this property to combine the two logs we get:
We now have the equation in the second form.
The next step with the second form is very simple. The only way these two base 2 logs can be equal is if the arguments are the same. So:
3x = x+7
This is a very easy equation to solve:
2x = 7
Checking solutions for equations like these is not optional! You must at least ensure that all arguments of logarithms remain positive. Use the original equation to check:
Checking :
We can already see that all three arguments are going to turn out positive. (If any arguments had turned out zero or negative we would have to reject the solution.) This completes the required part of the check. (You are welcome to finish the check to see if we made any mistakes.)
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