MHB Exponential and Logarithmic Problem

AI Thread Summary
The discussion focuses on solving the equation 2^x = 16(8^2x) for x. The user is struggling to start and has not successfully used logarithms to find the solution, which is known to be -4/5. Another participant suggests rewriting the equation using powers of 2, noting that 8 can be expressed as 2^3. The conversation emphasizes the need to convert all terms to a common base to facilitate solving the equation.
JoeC
Messages
2
Reaction score
0
I am looking for help solving for x for the question below. Any help would be greatly appreciated.

2^x=16(8^2x)
 
Mathematics news on Phys.org
JoeC said:
I am looking for help solving for x for the question below. Any help would be greatly appreciated.

2^x=16(8^2x)

What have you tried? Where are you stuck?
 
I don't really know where to start with this.

- - - Updated - - -

the answer to the question is -4/5 but I haven't been able to get it using log or ln.
 
JoeC said:
I am looking for help solving for x for the question below. Any help would be greatly appreciated.

2^x=16(8^2x)

JoeC said:
I don't really know where to start with this.

- - - Updated - - -

the answer to the question is -4/5 but I haven't been able to get it using log or ln.

Welcome to MHB, JoeC! :)

You have
$$2^x=16(8^{2x})$$
(Or at least that is what I assume you have.)

Since we have $2^x$, let's try to make the other power also a power of $2$.
We have that $8=2^3$.
Do you know what $(2^3)^{2x}$ is?
 

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 »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
View full post »

Similar threads

B Understanding exponentiation and logarithms together
Replies
12
Views
2K
MHB Solving for an exponential equation using logarithms 16^{x}-5(4)^{x}-6=0
Replies
3
Views
2K
MHB Exponential Equation solve 54⋅2^(2x)=72^x⋅√0.5
Replies
3
Views
2K
B Logarithmic growth vs exponential growth
Replies
4
Views
4K
B How to express ##3^{\sqrt(2)}## in terms of natural logarithms
Replies
10
Views
1K
Can I Use Logarithms to Solve Exponential Equations?
Replies
7
Views
2K
I Logarithmic scale - interpolation
Replies
2
Views
14K
Terminology for exponentiation and logarithms
Replies
1
Views
3K
B Characteristics of the parent logarithmic function
Replies
4
Views
2K
MHB Linear combination of sine and cosine function
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top