Question

question 3 (1 point)
the function $y = 5^x$ passes through the point.

a) (5, 1)

b) (5, -1)

c) (1, 5)

d) (-1, 5)
question 4 (1 point)
evaluate $e^{2 \ln 5}$.

a) 10

Explanation:

Question 3

Step1: Recall the function \( y = 5^x \)

To check if a point \((x, y)\) lies on the function, substitute \( x \) into the function and see if \( y \) matches.

Step2: Check option a) \((5, 1)\)

Substitute \( x = 5 \) into \( y = 5^x \), we get \( y = 5^5 = 3125
eq 1 \). So, a) is incorrect.

Step3: Check option b) \((5, -1)\)

Substitute \( x = 5 \), \( y = 5^5 = 3125
eq -1 \). So, b) is incorrect.

Step4: Check option c) \((1, 5)\)

Substitute \( x = 1 \) into \( y = 5^x \), we get \( y = 5^1 = 5 \). This matches the \( y \)-value of the point.

Step5: Check option d) \((-1, 5)\)

Substitute \( x = -1 \) into \( y = 5^x \), we get \( y = 5^{-1} = \frac{1}{5}
eq 5 \). So, d) is incorrect.

Step1: Use the logarithm power rule \( a\ln b=\ln(b^a) \)

So, \( 2\ln 5=\ln(5^2)=\ln(25) \). Then the expression becomes \( e^{\ln(25)} \).

Step2: Use the property \( e^{\ln x}=x \) (for \( x>0 \))

Since \( e^{\ln(25)} = 25 \) (because the exponential function and the natural logarithm are inverse functions).

Answer:

c) \((1, 5)\)

Question 4 (Assuming the expression is \( e^{2\ln 5} \), as there might be a typo)