MHB Exponential and Logarithmic Problem

Click For 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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

High School Understanding exponentiation and logarithms together
  • · Replies 12 ·
Replies
12
Views
2K
MHB Solving for an exponential equation using logarithms 16^{x}-5(4)^{x}-6=0
  • · Replies 3 ·
Replies
3
Views
2K
MHB Exponential Equation solve 54⋅2^(2x)=72^x⋅√0.5
  • · Replies 3 ·
Replies
3
Views
2K
High School Logarithmic growth vs exponential growth
  • · Replies 4 ·
Replies
4
Views
4K
High School How to express ##3^{\sqrt(2)}## in terms of natural logarithms
  • · Replies 10 ·
Replies
10
Views
2K
Can I Use Logarithms to Solve Exponential Equations?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Logarithmic scale - interpolation
  • · Replies 2 ·
Replies
2
Views
14K
Terminology for exponentiation and logarithms
  • · Replies 1 ·
Replies
1
Views
3K
High School Characteristics of the parent logarithmic function
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Am I misapplying something here? (Exponentials; Euler's identity)
  • · Replies 3 ·
Replies
3
Views
549