Make into one log function:
2logx-log4-log3+logx
do you have an answer?
two answers have been posted
2*log(x)-log(4)-log(3)+log(x)=2logx+logx-log4-log3
=3*log(x)-[log(4)+log(3)]
log(x^n)=n*log(x)
3*log(x)=log(x^3)
log(a)+log(b)=log(a*b)
log(4)+log(3)=log(4*3)=log(12)
log(a)-log(b)=log(a/b)
3*log(x)-[log(4)+log(3)]=log[(x^3)/12]
To rewrite the expression as a single logarithmic function, we can simplify and combine the logarithms using the properties of logarithms.
First, let's simplify each term:
2log(x) - log(4) - log(3) + log(x)
Using the power rule of logarithms, we can rewrite 2log(x) as log(x^2):
log(x^2) - log(4) - log(3) + log(x)
Next, we can use the quotient rule of logarithms to combine the terms with subtraction:
log[(x^2 * x) / (4 * 3)]
Simplifying the expression inside the logarithm:
log[(x^3) / 12]
Finally, we have expressed the given expression as a single logarithmic function:
log[(x^3) / 12]