8^(x+5)=32^(x-9)
To find the value of x in the equation 8^(x+5) = 32^(x-9), we can begin by simplifying both sides of the equation.
Let's start with the right side of the equation, 32^(x-9). We know that 32 can be written as 2^5. So, we can rewrite the equation as:
8^(x+5) = (2^5)^(x-9)
Using the property of exponents, we can multiply the exponents when raising one exponent to another exponent. So,
8^(x+5) = 2^(5*(x-9))
Now, let's simplify further by applying the power of a power rule. The power of a power rule states that when raising an exponent to another exponent, we can multiply the exponents. So,
8^(x+5) = 2^(5x-45)
Since the bases on both sides of the equation are the same (2), we can equate the exponents:
x + 5 = 5x - 45
We now have a linear equation in terms of x. Let's solve it by isolating the x term:
x - 5x = -45 - 5
-4x = -50
Dividing both sides of the equation by -4, we get:
x = (-50)/(-4)
x = 12.5
Therefore, the value of x in the equation 8^(x+5) = 32^(x-9) is 12.5.