The solution to this equation log₆(x) + log₆(3) = log₆( x+1) is x = 1/2.
What is a logarithm?
A logarithm is an exponent or power to which a base must be raised in order to produce a given number. If aˣ = n, then x is the logarithm of n to the base a, which is expressed mathematically as x = logₐn.
How to solve this problem?
We know that logₐx + logₐy = logₐ(xy)
Here, log₆(x) + log₆(3) = log₆( x+1)
i.e. log₆(3x) = log₆( x+1)
i.e. 3x = x + 1
i.e. 3x - x = 1
i.e. 2x = 1
i.e. x = 1/2
Therefore, the solution to this equation log₆(x) + log₆(3) = log₆( x+1) is x = 1/2. So, option A is correct.
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