Question

3^(x+1)-4*3^(x-2)=69

Answer 1

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Answer 2

To solve the equation 3^(x+1) - 4*3^(x-2) = 69, we can simplify the terms involving the exponential expression.

Let's rewrite the equation:

3^(x+1) - 4*3^(x-2) = 69

First, we can simplify the exponential terms:

3^x * 3^1 - 4 * (3^x / 3^2) = 69

Using the properties of exponents, we can simplify further:

3^x * 3 - 4 * (3^x / 9) = 69

Now, let's simplify the equation:

3^x * 3 - (4/9) * 3^x = 69

To combine the terms with a common base (3^x), we can factor it out:

(3 - (4/9)) * 3^x = 69

Simplifying the left side:

(27/9 - 4/9) * 3^x = 69

(23/9) * 3^x = 69

Next, divide both sides by (23/9):

3^x = 69 / (23/9)

To simplify the right side, we can multiply by the reciprocal:

3^x = 69 * (9/23)

Now, multiply the numbers on the right side:

3^x = (69 * 9) / 23

3^x = 621 / 23

To solve for x, we can take the logarithm of both sides with base 3:

log base 3 (3^x) = log base 3 (621/23)

Using the logarithmic property log base a (a^b) = b, we have:

x = log base 3 (621/23)

Calculating the value using a calculator or a logarithmic table, we find:

x ≈ 2.722

Therefore, the approximate solution to the equation 3^(x+1) - 4*3^(x-2) = 69 is x ≈ 2.722.