Answer:
x = -13/9
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