Algebra 2
posted by Peter .
Solve each equation below for x. (Use logarithms.)
10^(2x^(2)5x+11) = 10000
9^(2(x1)) = √(27)

just undo the operations, one by one:
10^(2x^(2)5x+11) = 10000
take log base 10
2x^(2)5x+11 = log10000 = 4
2x^2  5x + 7 = 0
(2x7)(x+1) = 0
. . .
9^(2(x1)) = √(27) = 3^(3/2) = 9^(3/4)
take log base 9
2(x1) = 3/4
8x8 = 3
8x = 11
. . .
Respond to this Question
Similar Questions

Math
Find an equation of the line that bisects the obtuse angles formed by the lines with equations 3xy=1 and x+y=2. a. (3√2 +√10)x(√10 + √2)y2√10+√2=0 b. (3√2  √10)x+(√10  √2)y+2√10+√2=0 … 
algebra 1
alright i have a few questions if its ok..? 
trigonometry
Use logarithms and the law of tangents to solve the triangle ABC, given that a=21.46 ft, b=46.28 ft, and C=32°28'30" Also Give checks. I know the use of logarithms is unnecessary but i have to show my solution by using logarithms … 
8th grade algebra: radicals
please help me solve these 1. 2√5/8 + 4√3/8  1/2√68 2. √4k5 +1=8 (the radical sign goes over 4k5) 3. (x+4)*2 /3 =8 4. Write the value of the discriminant of each equation. Then use it to decide how many different … 
maths
I will be thankfull to you if you help me to solve the below problem: 6√x11/3√x=2√x+1/√x+6 I tried to solve the above problem like this: (6√x11)(√x+6)=(3√x)(2√x+1) 6√x(√x+6)11(√x+6)=(3√x)(2√x)+(3√x)(1) … 
algebra/trig
1. which number below is irrational? a)√4/9 b) √20 c)√121 Why is the number you chose irrational? 
Algebra
Simplify the expressions and solve the equations 1. 2√3  √12 My answer: 2√3  2√3 = 0 2. √(5p + 5)^2 = √(6p + )^2 I got the answer p = 4 3. √(28) + √(63) + √(175) This one seems … 
8th grade algebra
Can you check my answers? 1. 3√20/√4 = 3√(5)(4)/2 = 3(2)√5/2 = 3√5 2. 4√15/√9 = 4√15/3 3. √12/√16 = √4(3)/4 = 2√3/4 = √3/2 4. √10/√5 = √2 
Algebra
1. Simplify the expression: 4√18+5√32 A.45√2 B.32√2 C.116√2 D.9√50 2. Simplify the expression: 7√53√80 A.5√5 B.4√75 C.5 D.4√75 3. Simplify the expression: √21(√3+√14) … 
Algebra  Check My Work
For Question 18 Simplify the Radical Expression ***  My Answer 1.√45 3√5*** 2.√180x^2 6x√5*** 3.√150x^3 k^4 5xk^2√6x*** 4.√21y * 5√49y 35y√21*** 5.(The square root sign applies …