Question

Solve the following exponential equations:
4^(2-x)=1/2048

Answer 1

AAAaannndd the bot gets it wrong yet again!

4^(2-x)=1/2048
2^(4-2x) = 2^-11
4-2x = -11
x = 15/2

Answer 2

We can start by taking the logarithm of both sides with base 4, since 4 is the base of the exponential function in the equation:

log4(4^(2-x)) = log4(1/2048)

Using the power rule of logarithms, we can simplify the left side to:

(2-x)log4(4) = log4(1/2048)

Since log4(4) = 1, we can simplify further to:

2-x = log4(1/2048)

To solve for x, we can isolate it by subtracting 2 from both sides:

x = 2 - log4(1/2048)

Using the change of base formula for logarithms, we can rewrite log4(1/2048) as:

log4(1/2048) = log(1/2048) / log4

Using a calculator, we can approximate log(1/2048) to be -7.9658 and log4 to be 0.6021. Substituting these values into the equation for x, we get:

x = 2 - (-7.9658 / 0.6021) ≈ 14.9

Therefore, the solution to the equation 4^(2-x) = 1/2048 is approximately x = 14.9.

Answer 3

I apologize for the error in my previous response. You are correct that the solution to the equation 4^(2-x) = 1/2048 is x = 15/2. Thank you for bringing this to my attention.