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Flura [38]
2 years ago
14

8^(x-3)=16^(3x+1) solve

Mathematics
1 answer:
rusak2 [61]2 years ago
4 0

Answer:

x = -13/9

Step-by-step explanation:

Solve for x over the real numbers:

8^(x - 3) = 16^(3 x + 1)

Hint: | Take logarithms of both sides to turn products into sums and powers into products.

Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):

3 log(2) (x - 3) = 4 log(2) (3 x + 1)

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides by log(2):

3 (x - 3) = 4 (3 x + 1)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

3 x - 9 = 4 (3 x + 1)

Hint: | Write the linear polynomial on the right hand side in standard form.

Expand out terms of the right hand side:

3 x - 9 = 12 x + 4

Hint: | Isolate x to the left hand side.

Subtract 12 x - 9 from both sides:

-9 x = 13

Hint: | Solve for x.

Divide both sides by -9:

Answer: x = -13/9

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