Question

How do you start to solve log(ln(4-x))=1/3

Answer 1

so log id the opposite of power. log(x) = y is basically saying "to what power of 10 do i need to get x?". that is "y". like say you have log(100) = y. this means that "y" is the power that you put unto 10 to get 100. thus, in this example, y = 2. on to the problem.

to reverse a log, you need to raise the entire two sides of the equation to the same power (in this case 10), like so:
\[\log(\ln(4-x)) = \frac{ 1 }{ 3 }\]
\[10^{\log(\ln(4-x))}=10^{\frac{ 1 }{ 3 }}\]
this will cancel out the log and the power of 10 on the left side, giving you:
\[\ln(4-x)=10^{\frac{ 1 }{ 3 }}\]

"ln" is the same thing as log, but using a base of "e" instead of 10. to reverse it, just raise both side of the equation to the same power gain (in this case "e"):
\[e^{\ln(4-x)}=e^{10^{\frac{1}{3}}}\]
again, the "ln" and the power of "e" on the left side cancel out. so, you have:
\[4-x=e^{10^{\frac{1}{3}}}\]
\[x=4+e^{10^{\frac{1}{3}}}\]
so x is about equal to 12.623

Answer 2

That's almost right. Except 4 is positive do you have to subtract it from the other side. And x is negative...

Answer 3

lol yeah you're right
i cant read signs