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Solve for b.

8^b^-^1 = 2^4^b^+^4

User Carmelle
by
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1 Answer

4 votes

Final answer:

To solve the equation for b, we rewrite 8 as 2^3, express both sides with the base of 2, and equate the exponents. The equation simplifies to 3b-3 = 4b+4. Solving this linear equation, we find that b = -7.

Step-by-step explanation:

To solve the equation 8^b^-^1 = 2^4^b^+^4, we need to express both sides with the same base and then equate the exponents.

Since 8 is 2^3, we can rewrite 8^b as (2^3)^b. Hence, our equation becomes:

(2^3)^(b-1) = 2^(4b+4)

Simplifying the left side by multiplying the exponents gives:

2^(3b-3) = 2^(4b+4)

Now that both sides have the same base, we can equate the exponents:

3b - 3 = 4b + 4

Subtracting 4b from both sides:

-b - 3 = 4

Adding 3 to both sides:

-b = 7

Finally, multiplying by -1 to solve for b:

b = -7

User Yi Feng Xie
by
8.6k points

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