### Logarithm Equation Function

E^x*e^x+1=e^x-1

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E^x*e^x+1=e^x-1

3^(2x-1)=5x

10^x=200

5^x-8=23

Ln (under radical)=1 (x+2)

Solve for x in the following logarithmic equation. Please show a detailed step by step solution. logx - log2 = 5

Simplify the Expression [ (3(x^4)(y^2))/(2(x^7)(y^6))^3 x ((2x^-2)(y^4))^5 / ((3x^3)(y^-2))^5 ]^1/2 Make sure to show all steps.

Given that S=(R+D)^(1/3) and T=(R-D)^(1/3) where D= square root(R^2+Q^3), show that ST=-Q

Hi, can someone please explain to me how sqrt (square root of)128 becomes 8sqrt2 ; or sqrt68 becomes 2sqrt17? ; or sqrt45 becomes 3sqrt5? Thank you

Simplify the following expressions: a. 3x-2/2x2+x-3 Divide by 9x-6/2x-2 b.(108)1/2- (48)1/2+ (192)1/2 (should be exponent 1/2) c. (20x3+3x2-4x+5)/(4x2+3x-7) (should be exponent 3 and 2,2).

Factor the following: a. 81a4- 16b4 (should be exponent 4) b. 12x2+ x- 35 (should be exponent 2)

3 years ago, Liz's age was 1/3 of her mother's age. Now, 7 years later, her age will be 1/2 of her mother's age. How old are Liz and her mother?

Please see the attached file for full problem description. I would like to get some assistance in setting up this problem. A=1.645 and they give the answer of x as .56506.

Logarithms and exponents. See attached file for full problem description. Q1: Express in log form 82=64 Q2: express in exponential form log4256=4 Q3: find unknown log327=x Q4: express as sum diff or multiple logarithm a. log314 b. log2 5/10 c. log5 (n3) Q5: express as log of single quantity a. long23 + log22

For the given functions f and g, find: (a) the composition of (f o g) (4) (b) (g o f) (2) (c)( f o f)(1) (d) (g o g) (0) f(x) = x3/2; g(x) = 2 / x + 1 *note: x3/2 is actually a square root number but I couldn't figure out how to make the numbers small.

For the given functions f and g, find: (a) the composition of (f o g) (4) (b) (g o f) (2) (c)( f o f) (1) (d) (g o g) (0) f(x) = 2x; g(x) = 3xsquared + 1

For the given functions f and g, find the following functions and state the domain of each. (a) f + g (b)f - g (c)f x g (d) f / g f(x)= square root of x + 1; g(x) = 2 / x

For the given functions f and g, find the following functions and state the domain of each. (a) f + g (b)f - g (c)f x g (d) f / g f(x) = 2xsquared + 3; g(x) = 4xcubed + 1

Sketch the graph of each function. Be sure to label three points on the graph. If f(x) = integral (2x), find: (a) f(1.2) (b) f(1.6) (c) f(-1.8)

Please help me with #4, #10, and #16. I am having trouble woth these. Please show your work so that I may better understand the process.

Solve: x3 - 2x2+x=-5(x-1)2.

Let m be the smallest positive integer such that @^m=E for all @eS_n. Show that m=lcm(2,3,4,5,...,n).

What is the additive principle? Please provide simple examples.

Assume that the sum and product of two roots of a quadratic equation are 5 and 6, respectively. Find two roots.

I am asked to verify Fubini's Theorem for an integral evaluated over an equilateral triangle. I am asked to fully discuss the reasons for the limits of integration in my solution. See attached file for full problem description.

Factor: 9q^2-72q+750.

Test the following for divisibility by 2,3,4,5,6,8,9,and 10. (No calculator, explain your thinking). i. 6 543 210 b. What is the smallest whole number that is divisible by 2,3,4,5,6,8,9 and 10.

Simplify each of the following expressions further and identify the number property(ies) used in each. 1. 2 x (15+8)= (2 x 15)+ (2 x 8)= 2. 5/2 x (3/4 x 2/5)= (5/2 x 2/5)x 3/4=

Show by induction that: a) Sum(n^2/[(2n-1)*(2n+1)],n=1..) = n(n+1)/[2*(2n+1)] b) Sum( r/(r-1)!, r=1..n) = 1-1/(n+1)! c) n^3+3n^2-10n is divisible by 3 d) 4^(2n+1) + 3^(n+2) is divisible by 13 See attached file for full problem description.

Please see the attached file for the fully formatted problems. Find the following: a) The coefficient of x in the expansion of b) The coeffiecient of in the expansion of c) The coefficient of in the expansion of d) The coefficient of in the expansion of is equal to the coefficient of in the