Just be aware that even calculators use approximations for logarithms so the two sides may not be exactly equal. (You can check this with your calculator. I like to get rid of fractions by multiplying both sides of the equation by the Lowest Common Denominator (LCD) of all the fractions. Rewrite the equation in exponential form:.Use the third property on the left side creating a very complex fraction:.Subtract one of the logs from each side.

If this does not make sense to you then you can take the long route: If two values are equal then their logs are equal (and vice versa). If the log of (x-6)/3 is equal to the log of (x+2)/2, then (x-6)/3 must be equal to (x+2)/2. A bit of logic will take us through the next step. log(5) + log(2) log ( 5) + log ( 2) Use the product property of logarithms, logb(x)+ logb(y) logb(xy) log b ( x) + log b ( y) log b ( x y). The equation is now in one of the desired forms.

We will use the third property on both sides of your equation to combine the two logs into one: There are also no additions of logs so we will not need the second property. In your problem, the logs have no coefficients so we will not need the first property. We use the first property to get rid of coefficients, if any, before using these last two properties.) (Note that these two properties require no coefficients (IOW coefficients of 1) in front of the logs. The other two allow us to combine the addition or subtraction of logs into a single log. The first one allows us to move a coefficient in front the log function into the argument as an exponent. In order to do this we need to understand the properties of logarithms: So we need to condense the two logarithms on each side into one. log(x)+log(2)log(2x) In general, loga(x)+loga(y) loga(xy) (see below for explanation). In order to solve equations where the variable is in the argument of a logarithm, you need to modify the equation, using the properties of logarithms and proper Algebra, into one of the following forms: is not a multiplication and it is incorrect to use the Distributive Property on it like you have. stands for the result or output of the log function when the input is (x-6). 'log' is the name of the logarithm function. When I attempted this question I expanded the brackets so that the equation wasĪs you already found out, this is not correct. You can put this solution on YOUR website!

Condense log x times log2