Question

Log3 (4x-6)= log3 2+3

Answer 1

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Answer 2

To solve the equation log₃(4x - 6) = log₃(2) + 3, we can use the properties of logarithms. The basic property we'll use here is that if logₐ(b) = logₐ(c), then b = c.

Step 1: Apply the property of logarithms to remove the logs on both sides of the equation:

log₃(4x - 6) = log₃(2) + 3

Step 2: Since the bases of the logarithms are the same (both are log base 3), the arguments inside the logarithms must be equal:

4x - 6 = 2 + 3

Step 3: Simplify the right side:

4x - 6 = 5

Step 4: Now, isolate the variable x:

4x = 5 + 6

4x = 11

Step 5: Divide both sides by 4 to solve for x:

x = 11/4

So, the solution to the equation is:

x = 11/4