log base 2 (3r+5)= 5

To solve the equation log base 2 (3r+5) = 5, we need to isolate the variable r. Here's how you can do it step by step:

Step 1: Rewrite the equation in exponential form.
In logarithmic form, log base 2 (3r+5) = 5 means that 2 raised to the power of 5 equals 3r+5. So we have: 2^5 = 3r+5.

Step 2: Simplify the exponential form.
2^5 = 32, so the equation becomes: 32 = 3r+5.

Step 3: Solve for r.
Now, we need to isolate r. Start by subtracting 5 from both sides of the equation: 32 - 5 = 3r. This simplifies to: 27 = 3r.

Step 4: Divide both sides by 3 to solve for r.
Divide both sides of the equation by 3: 27/3 = r. This simplifies to: 9 = r.

Therefore, the solution to the equation log base 2 (3r+5) = 5 is r = 9.