Posted by Angelina on Friday, January 30, 2009 at 2:37am.
Help with these problems would be greatly appreciated:
1.Find the definite integral of dx/(x(1+ln(x))from e^6 to 1.
2. Solve for x in terms of k for log[2,x^6)+log[2,x^10=k. (its log base 2)
3.Solve log base 3(log base 3, x)=-2
- Calculus - beyond me - Damon, Friday, January 30, 2009 at 3:13am
Perhaps it is the lateness of the hour but I am stuck on the first one.
- Math - drwls, Friday, January 30, 2009 at 4:13am
1. For the indefinite integral, try the substitution ln x = u
e^u = x
e^u du = dx
indef. integral of dx/(x(1+ln(x))
= integral of e^u du/[e^u*(1 + u)
= integral of du/(1+u)
= ln (1 + u) = ln (1 + ln x)
When x = e^6, the indef. integral is ln (1 + 6) = ln 7 = 1.9459
When x = 1, the indef. integral is ln 1 = 0
Def. integral = -ln 7
3. Rewrite as
3^-2 = log3,x = 1/9
3^(1/9) = x
x = 1.129831
- Math - Reiny, Friday, January 30, 2009 at 10:12am
2. log2 x^6 + log2 x^10 = k
6log2x + 10log2x = k
16log2x = k
log2x^16 = k
2^k = x^16
x = 2^(k/16)
Answer this Question
More Related Questions
- Advanced Functions/ Precalculus Log - 1. Evaluate 4^(log base4 64) + 10^(log100...
- Algebra 2 - -Explain the difference between log base b (mn) and ( log base b of ...
- math - Logarithm!!! Select all of the following that are true statements: (a) ...
- check! - here is the question: log5(x-4)= log7x solve for x. These are just base...
- Trig - log base b 64 - log base b 16 = log base 4 16 solve for the variable.. i...
- Precalc - 1. 1/3log base 8 of (x+1)=2log base 8 of 3-(2/3)log base 8 of (x+1) 2...
- math - write as a single logarithm: -2logbase3(1/x)+(1/3)logbase3(square root of...
- math(Please help) - 1) use the properties of logarithms to simplify the ...
- Math - h(x) = log (6x+5/7x-4) Find a formula for the inverse function h^-1(x) h...
- math - Q1:solve log(5)x-log(25)(x+10) = 0.5 Q2:If 2log(a)x=1+log(a) (7x-10a) ,...