Question 4 asks for the first step in solving the equation $8 + log_3(2x + 5) = 40$ differently from solving $log_3(2x + 5) = 40$. Question 5 asks to solve the equation $e^x = 10$ using the natural log, and to provide the answer accurate to 2 decimal places.

1. Problem Description

Question 4 asks for the first step in solving the equation $8 + log_3(2x + 5) = 40$ differently from solving $log_3(2x + 5) = 40$.

Question 5 asks to solve the equation $e^x = 10$ using the natural log, and to provide the answer accurate to 2 decimal places.

2. Solution Steps

Question 4:

The main difference between the two equations is the presence of the constant 8 in the first equation. To isolate the logarithmic term in the first equation, we need to subtract 8 from both sides. The second equation already has the logarithmic term isolated. Therefore, the first step in solving $8 + log_3(2x + 5) = 40$ is to subtract 8 from both sides. Transforming $8 + log_3(2x+5) = 40$ into $log_3(8(2x+5)) = 40$ is incorrect since $8$ is not multiplied by $log_3(2x+5)$.

Question 5:

To solve $e^x = 10$, we take the natural logarithm (ln) of both sides:

$ln(e^x) = ln(10)$

Since $ln(e^x) = x$, we have:

$x = ln(10)$

Using a calculator, $ln(10) \approx 2.302585$.

Rounding to two decimal places, we get $x \approx 2.30$.

3. Final Answer

Question 4:

You have to subtract 8 from both sides first.

Question 5:

2.30