If 8^m=1/4 -2^3m. Find m

Answer 1

We can write 1/4 as 2^(-2), so the equation becomes:

8^m = 2^(-2) - 2^(3m)

We know that 8 can be written as 2^3, so we can substitute that in:

(2^3)^m = 2^(-2) - 2^(3m)

Simplifying the left-hand side using the power of a power rule:

2^(3m) = 2^(-2) - 2^(3m)

Now we can combine the two terms on the right-hand side, since they have the same base:

2^(3m) = 2^(-2-3m)

Using the rule that a^(−n) = 1/a^n:

2^(3m) = 1/2^(2+3m)

Multiplying both sides by 2^(2+3m):

2^(5m+2) = 1

Now we can solve for m by taking the logarithm base 2 of both sides:

5m + 2 = log2(1)

Since log2(1) = 0, we get:

5m + 2 = 0

Solving for m:

m = -2/5

Therefore, m = -0.4.

Answer 2

AAAaannndd the bot gets it wrong yet again!

2^(3m) = 2^(-2-3m)
2^(6m+2) = 1
6m+2 = 0
m = -1/3

Answer 3

My apologies for the mistake in my previous response. You are correct that the equation simplifies to:

2^(3m) = 2^(-2-3m)

Taking the logarithm base 2 of both sides, we get:

3m = -2-3m

Simplifying and solving for m:

6m = -2

m = -1/3

Thank you for bringing this to my attention.