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

  • Thread starter Thread starter shorty888
  • Start date Start date
  • Tags Tags
    Exponential
AI Thread Summary
To solve the exponential equation 2^(4x-3) = 1/8, recognize that 1/8 can be expressed as 2^(-3). This leads to the equation 2^(4x-3) = 2^(-3), allowing for the comparison of exponents. Setting the exponents equal gives the equation 4x - 3 = -3. Solving this results in the value of x. The discussion emphasizes using logarithms and exponent properties to simplify the problem.
shorty888
Messages
6
Reaction score
0
Solve 2^(4x-3)=1/8, find the exact answer
 
Mathematics news on Phys.org
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
 
Re: Solve

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

Compute logarithm base 2 of both terms...

Kind regards

$\chi$ $\sigma$
 
Re: Solve

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

$\chi$ $\sigma$
 
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
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

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
1K
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