SOLUTION: 3(log6 base x+ log6 base3)+4=10
How do you distribute the 3 out? My math teacher can't explain it at all.
Algebra.Com
Question 720475: 3(log6 base x+ log6 base3)+4=10
How do you distribute the 3 out? My math teacher can't explain it at all.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
I'm assuming that the equation is not what you said. I think the equation is:
is "the base 6 log of x" and is "the base 6 log of 3". If you really meant what you posted then a) I'm sorry, but you'll have to re-post your question and b) the problem is quite difficult.
When solving equations where the variable is in the argument of a logarithm usually starts by transforming the equation into one of the following forms:
log(expression) = number
or
log(expression) = log(expression)
Your equation has several "non-log" terms so it will more difficult to transform it into the "all-log" second form. So we will aim for the first form. This form has a single log. So we want to find a way to combine the two logs we have into one.
The two logs we have are not like terms so we cannot just add them. (Like logarithmic terms have the same bases and arguments. Our logs have the same bases but the arguments, x and 3, are different.) Fortunately there is another way to combine the two logs. A property of logarithms, , shows us how we can combine two logs which ...which have the same base- have coefficients of 1
- have a "+" between them.
Our logs fir all three requirements. So we can use the property giving us:
or
The form, log(expression) = number, has the log all by itself. So we need to get rid of the 3 and the 4. Subtracting 4 we get:
Dividing by 3:
We finally have the desired form.
The next step with this form is to rewrite the equation in exponential form. In general is equivalent to . Using this pattern on our equation we get:
which simplifies to:
One more step: divide by 3:
When solving equations like this, where the variable started in the argument of a log, it is not optional to check. You must ensure that all arguments of all logs are valid when the variable is equal to what you think is the solution. (Valid arguments are positive.) If an argument becomes invalid, you must reject that solution.
Use the original equation to check:
Checking x = 12:
We can see that both arguments are positive. So our solution passes the check.
RELATED QUESTIONS
Hey guys, I'm having a bit of trouble finding out a few things about the graph of y =... (answered by ccs2011)
How do you condense log6^3+2... (answered by Fombitz)
how do i solve log6 3 + log6 8 - log6... (answered by Gogonati)
log6(x+3) +... (answered by Nate)
log6(x-3)+log6(x-4)=-2 (answered by rapaljer)
how do you solve:... (answered by MathLover1)
Can you please help explain step by step of how to a problem like... (answered by edjones)
Hi I couldnt figure out how to do this problem... (answered by stanbon)
Hi, how do you solve log6 9 + log6 x =... (answered by MathLover1)