Discussion Topic

# Solving equations involving real values of t

Summary:

Solving equations involving real values of \( t \) generally requires isolating \( t \) by performing algebraic operations such as addition, subtraction, multiplication, division, and using functions like square roots or logarithms. The specific steps depend on the equation's form, but the goal is to express \( t \) in terms of other known quantities, ensuring all operations are valid for real numbers.

## Expert Answers

Solve for real t 11^(t+1) -1=4*11^t

We have to solve 11^(t+1) -1=4*11^t for t.

11^(t+1) -1=4*11^t

=> 11^t*11 - 1 = 4*11^t

let 11^t = x

=> 11x - 1 = 4x

=> 7x = 1

=> x= 1/7

11^t = 1/7

Here the bases are different, so we have to use the log function.

log 11^t = log (1/7)

=> t* log 11 = -log 7

=> t = -log 7 / log 11

The required value of t is -log 7 / log 11

Last Updated on

Solve the equation t^4+10t-11=0

It is not possible to solve the equation you have given t^4 + 10t - 11 = 0.

Instead, here is the solution for t^4 + 10 t^2 - 11 = 0

let t^2 = x

=> x^2 + 10x - 11 = 0

=> x^2 + 11x - x - 11 = 0

=> x(x + 11) - 1(x + 11) = 0

=> (x - 1)(x + 11) = 0

=> x = 1 and x = -11

t^2 = 1

=> t1 = 1

=> t2 = -1

t^2 = -11

=> t3 = i*sqrt 11

=> t4 = -i*sqrt 11

The solutions of the equation t^4 + 10 t^2 - 11 = 0 are {-1 , 1, i*sqrt 11, -i*sqrt 11}

## See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Last Updated on