Solve:
3^5x = 27^(x-1)
3^5x = 27^(x-1).
3^5x = (3^3)^(x-1)
3^5x = 3^(3(x-1))
3^5x = 3^(3x-3)
5x = 3x-3
5x-3x =-3
2x = -3
X = -3/2 = -1.5.
thank you!
To solve the equation 3^(5x) = 27^(x-1), we can start by expressing 27 as 3^3, since both sides of the equation have the base 3.
Rewriting the equation:
3^(5x) = (3^3)^(x-1)
Using the properties of exponents, we can simplify the right side of the equation:
3^(5x) = 3^(3(x-1))
Since the bases are the same, we can equate the exponents:
5x = 3(x - 1)
Now let's solve for x:
5x = 3x - 3
Subtracting 3x from both sides:
2x = -3
Dividing both sides by 2:
x = -3/2
Therefore, the solution to the equation 3^(5x) = 27^(x-1) is x = -3/2.