Exponential and Logarithmic Problem

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Discussion Overview

The discussion centers around solving the equation \(2^x = 16(8^{2x})\). Participants are seeking assistance with the mathematical steps involved in finding the value of \(x\), particularly using logarithmic methods.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about where to start with the problem.
  • Another participant suggests that the answer is \(-4/5\) but indicates difficulty in arriving at this solution using logarithmic functions.
  • A later reply proposes rewriting the equation in terms of powers of \(2\) to facilitate solving, specifically mentioning that \(8\) can be expressed as \(2^3\) and questions the participant's understanding of exponentiation.

Areas of Agreement / Disagreement

There is no consensus on the solution process or the correctness of the proposed answer, as participants are still exploring different approaches to the problem.

Contextual Notes

Participants have not fully detailed their attempts or the specific steps they have taken, leading to some ambiguity in the discussion.

JoeC
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I am looking for help solving for x for the question below. Any help would be greatly appreciated.

2^x=16(8^2x)
 
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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?
 

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