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. log_{2} x^6 + log_{2} x^10 = k

6log_{2}x + 10log_{2}x = k

16log_{2}x = k

log_{2}x^16 = k

2^k = x^16

x = 2^(k/16)

## Answer this Question

## 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) ,...