# What is a if log(base3)2+log(base3)a=1?

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### 1 Answer

You need to convert the summation of logarithms into the logarithm of product, such that:

`log_3 2 + log_3 a = log_3 (2a)`

Since `log_3 2 + log_3 a = 1` , you need to replace `log_3 (2a)` for `log_3 2 + log_3 a,` such that:

`log_3 (2a) = 1 => 2a = 3^1 => a = 3/2`

Since a is the argument of logarithms, it needs to be positive, hence, `a = 3/2 ` is valid.

**Hence, evaluating the value of a, under the given conditions, yields **`a = 3/2.`