How Do You Solve the Exponential Equation 2^(4x-3) = 1/8?

  • MHB
  • Thread starter shorty888
  • Start date
  • Tags
    Exponential
In summary, to solve the equation 2^(4x-3)=1/8 and find the exact answer, you can use the fact that 1/8 is equal to 2^-3. By taking the logarithm base 2 of both sides, you can simplify the equation to 4x-3=-3. This is equivalent to a first-order algebraic equation, which can be solved to find the exact answer.
  • #1
shorty888
6
0
Solve 2^(4x-3)=1/8, find the exact answer
 
Mathematics news on Phys.org
  • #2
Re: Solve

shorty888 said:
Solve 2^(4x-3)=1/8, find the exact answer

Since \(1/8=2^{-3}\), you want to solve:

\(2^{4x-3}=2^{-3}\)

so, now can you do it?

CB
 
  • #3
Re: Solve

shorty888 said:
Solve 2^(4x-3)=1/8, find the exact answer

Compute logarithm base 2 of both terms...

Kind regards

$\chi$ $\sigma$
 
  • #4
Re: Solve

No, I don't understand.. I can't do it.. How??
 
  • #5
Re: Solve

shorty888 said:
No, I don't understand.. I can't do it.. How??

You have $\displaystyle a=b \implies \log_{2} a= \log_{2} b$, so that $\displaystyle a=2^{4x-3},\ b=\frac{1}{8} \rightarrow 4x-3=-3$ and we have a first order algebraic equation...

Kind regards

$\chi$ $\sigma$
 
  • #6
Re: Solve

shorty888 said:
No, I don't understand.. I can't do it.. How??

In future please quote which post you are responding to (use the reply with quote option).

If you are referring to my post, the exponents on both sides are equal so: \(4x-3=-3\)

This is essentially the same as chisigma's method.

CB
 

FAQ: How Do You Solve the Exponential Equation 2^(4x-3) = 1/8?

What is an exponential equation?

An exponential equation is an equation in which the variable appears in the exponent, such as y = ab^x. It is used to model situations where a quantity grows or decays at a constant rate.

How do you solve an exponential equation?

To solve an exponential equation, you can use logarithms or rewrite the equation in a different form. If the bases of the exponential terms are the same, you can set the exponents equal to each other and solve for the variable. If the bases are different, you can use logarithms to bring the variable out of the exponent and solve for it.

What are the rules for solving exponential equations?

There are several rules for solving exponential equations, including:

  • When the bases of the exponential terms are the same, you can set the exponents equal to each other and solve for the variable.
  • When the bases are different, you can use logarithms to bring the variable out of the exponent and solve for it.
  • When the variable appears in both the base and the exponent, you can use the power rule to simplify the equation.
  • If the equation has a base of e (the natural logarithm), you can use the ln function to solve for the variable.

Can you solve exponential equations with negative exponents?

Yes, you can solve exponential equations with negative exponents. Negative exponents represent fractions with the variable in the denominator. To solve, you can use the power rule to bring the variable to the numerator and then solve as you would a regular exponential equation.

What are some real-life applications of exponential equations?

Exponential equations are commonly used in science, finance, and engineering to model situations where a quantity grows or decays at a constant rate. Some real-life applications include population growth, radioactive decay, compound interest, and bacterial growth.

Similar threads

MHB Absolute Value Equation |3x - 2|/|2x - 3| = 2
Replies
10
Views
2K
MHB How to Evaluate the Infinite Sum for 0 < x < 1?
Replies
6
Views
2K
MHB Solutions of an inequality (1-√(1-4x^2)/x < 3
Replies
4
Views
2K
MHB How can I solve more complex exponential equations?
Replies
2
Views
1K
MHB -s6.6 solve exponential eq 3^x-14\cdot 3^{-x}=5
Replies
1
Views
840
MHB Exponential Equation solve 54⋅2^(2x)=72^x⋅√0.5
Replies
3
Views
2K
MHB Exponential Equations solve 27^x=1/√3
Replies
2
Views
2K
MHB [ASK] A Line Intercepting A Circle
Replies
4
Views
1K
MHB Maximizing $y=|4x^3+ax^2+bx+c|$ in $[-1,1]$
Replies
1
Views
1K
MHB Linear combination of sine and cosine function
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top