logarithms
posted by Jennifer .
Solve the logarithm equation. Express the solution in exact form only.
log[6](64x^3+1)log[6](4x+1)=1

log[6] ( (64x^3 + 1)/(4x+1) ) = 1
(64x^3+1)/(4x+1) = 6^1
I can reduce the left side ...
(4x+1)(16x^2 4x+1)/(4x+1) = 6
16x^2  4x  5 = 0
x = (4 ± √336)/32
but in log (4x+1) , 4x+1 > 0
x > 1/4, so we have to reject the negative x value
x = (4 + √336)/32
= (4 + 4√21)/32
= (1 + √21)/8
Respond to this Question
Similar Questions

algebra
logarithms Solve the following equations 3^x2=6 Add 2 to both sides of the equation to start. Whatever operation you do to one side of an equation you must do to the other side as well. 3^x  2 + 2 = 6 + 2 3^x = 8 Changing to logs: … 
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) … 
calculus
Please help me solve this equation. log[2](3)+log[2](x)=log[2](5)+log[2](x2) 1. Solve equation by setting up algebraically. 2. Use appropriate properties of Logarithm to reduce the number of logarithmic terms to only one. 3. Solve … 
Math  Logarithm
Solve the following logarithm equation. Please show all of your work. log (5 + x) – log(x – 2) = log 2 
pre calculous
use the properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. show your work ln x^2/y^3 Assuming x,y AND z are positive use properties of logariths to write the expression … 
College Algebra
Solve the logarithmic equation. Express your solutions in exact form only. Please show all of your work. log base 6 (64x^3+1)log base 6 (4x+1)=1 
math
Use the Laws of logarithms to rewrite the expression log(base 2)(11x(x9)) in a form with no logarithm of a product, quotient or power. After rewriting we will have: log(base 2)A+log(base 2)x+log(base 2)f(x) What is A and what is f(x)? 
Math
Find the exact solution, using common logarithms, and a twodecimalplace approximation of each solution. log(7x + 4) = 2 + log(2x − 3) Solve the equation. log(x^3) = (log x)^2 
Advanced Functions/ Precalculus Log
1. Evaluate 4^(log base4 64) + 10^(log100) 2. Write 1+log(base2)x^3 as a single logarithm 3. Write log(base b)√(x^3 y z^6) 4. Solve log(base 2)xlog(base 2)6=log(base 2)5+2log(base 2)3 5. Solve 3^(2x) = 9(81^x) 6. Solve 3^(2x)=7^(3x1). … 
Logarithm help
using logarithms to solve exponential equations. 5^1+x = 2^1x I need exact numbers. I did one on my own already. 5^x1 = 9 5^x1 = 9 log(5^x1) = log9 (log5)(x1) = log9 x1 = (log9/log5) x= (log9/log5)1 x = 2.3652 Logarithm help …