Question

3^(х-1)-3^(х)+3^(х+1)=63

Answer 1

$3^{x} : 3 -3^x+3^x*3=63 \\ \\3^x(\frac{1}{3}-1+3)=63 \\ \\ 3^x*2 \frac{1}{3}=63 \\ \\ 3^x=63*\frac{3}{7} \\ \\ 3^x=3*3*3$

Answer 2

To solve the equation 3^(x-1) - 3^x + 3^(x+1) = 63, we can simplify the equation using the properties of exponents.

Let's rewrite the equation step by step:

3^(x-1) - 3^x + 3^(x+1) = 63

First, let's simplify the exponents:

(1/3) * 3^x - 3^x + 3 * 3^x = 63

Next, let's combine like terms:

[(1/3) - 1 + 3] * 3^x = 63

Simplifying further:

(1/3 + 2) * 3^x = 63

(7/3) * 3^x = 63

Now, let's isolate the exponential term:

3^x = 63 * (3/7)

3^x = 27

To solve for x, we need to take the logarithm of both sides. Let's take the logarithm base 3 of both sides:

log3(3^x) = log3(27)

x = log3(27)

x = log3(3^3)

x = 3

Therefore, the solution to the equation 3^(x-1) - 3^x + 3^(x+1) = 63 is x = 3.