# If `log_2 x = 6` and `log_3 y = 4` what is `log_12 xy`

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### 1 Answer

It is given that `log_2 x = 6` and `log_3 y = 4` .

`log_2 x = 6` and `log_3 y = 4`

=> `x = 2^6` and `y = 3^4`

`log_12(x*y)`

= `log_12(2^6*3^4)`

= `log_12 (12^3*3)`

Use the property `log(a*b) = log a + log b`

= `log_12 12^3 + log_12 3`

Use the property `log a^b = b*log a` and `log_b b = 1`

= `3 + log_12 3`

`~~ 3.4421`

**The value of **`log_12(x*y) = 3 + log_12 3`