# Math

posted by .

Can you show me the work to get these answers also?

A.Solve each equation. Leave exact answers:
1.5^3x-2=14
2.log(x-1)-logx=log(x-3)

B.If f(x)=x+2/x and g(x)=7/x-5,
a. Find the composition (f o g)(x) and simplify completely.
b. Find the domain of (f o g)(x).Write answer in interval notation.
c. Find the composition of (g o f)(x) and simplify completely.
d. Find the domain (g o f)(x).Write your answer using interval notation.

• Math -

1. 0.5^3x-2 = 14
0.5^3x = 14+2 = 16
Take Log of both sides:
3x*Log 0.5 = Log 16
Divide both sides by Log 0.5:
3x = Log 16/Log0.5 = -4
Divide both sides by 3:
X = -4/3

2. Log(x-1)-Log x = Log(x-3)
Log((x-1)/x) = Log(x-3)

B. f(x) = (x+2)/x; g(x) = 7/(x-5)

a. F(g(x)) = (7/(x-5)+2)/(7/(x-5)) =
(7+2(x-5)/(x-5))/(7/(x-5)) =
((2x-3)/(x-5))/(7/(x-5)) =
((2x-3)/(x-5))*(x-5)/7 = (2x-3)/7.

b. Domain: All real values of X.
-Infinity < X < +Infinity.

c. g(F(x)) = 7/((x+2)/x-5)=
7/(x+2-5x)/x = 7/(x+2-5x)/x =
7/(2-4x)/x = 7x/(-2(2x-1))

d. 2x-1 = 0
2x = 1
X = 1/2 Will result in a denominator of zero and the Eq becomes undefined.

DOMAIN: All real values of X except 1/2.
X <> 1/2.

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### math

solve for x without using a calculator 5^(x+1) = 25 i know that x would equal 1 because 5^2 is 25, but i don't know how to show how to solve it All you need to do is what you just did: Explain that if x = 1, the equation is satisfied. …
2. ### check math

Here are my answers. Can you check if I got the right answers?
3. ### math -- log and exp. functions

1. evaluate log(base2)[(1/32) X 4^-9] 2. simplify: log x^2 y - (1/2)logx + 3 log y
4. ### algebra homework

please check my answers. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. ln sqrt x+6 = 9 i got {e^9-6} log (x + 4) = log (5x - 5) …
5. ### Math

these are some problems i do not get any help is appreciated. These are copied exactly from the worksheet so i don't think i wrote anything wrong. Please explain it for me and could i get the answer thanks (: Log7 x= ½ log7 36 (log …
6. ### math

Logarithm!!! Select all of the following that are true statements: (a) log(2x) = log(2) + log(x) (b) log(3x) = 3 log(x) (c) log(12y) = 2 log(2) + log(3y) (d) log(5y) = log(20y) – log(4) (e) log(x) = log(5x) – log(5) (f) ln(25) …
7. ### math

Wondering the answers to these: Find the value of each of the following. Leave your answers as fractions where appropriate. [I did these myself but need to answer-check] a) log[base4](1/8) b) 10^(-10log3) c) 2log[base3](9) d) log[base3](3)^(2x) …
8. ### Math

Find the exact solution, using common logarithms, and a two-decimal-place approximation of each solution. log(7x + 4) = 2 + log(2x − 3) Solve the equation. log(x^3) = (log x)^2
9. ### Math

h(x) = log (6x+5/7x-4) Find a formula for the inverse function h^-1(x) h^-1(x) = My work so far h(x) = log(6x+5/7x-4) y=log(6x+5/7x-4) x=log(6y+5/7y-4) 7xy-4x= log(6y+5) how would I solve from here. Would I solve for y then do the …
10. ### precalc

Suppose that u=log(2) and v=log(5). Find possible formulas for the following expressions in terms of u and/or v. Your answers should NOT involve any log's. a) log(0.4)= b) log(0.08)= c) log(2500)=

More Similar Questions