If 2^x = 3^y = 6 then which of the following statements is true?

```
1) x - y = xy
2) y - x = xy
3) x + y = xy
4) xy = x/y
```

+2 votes

If 2^x = 3^y = 6 then which of the following statements is true?

```
1) x - y = xy
2) y - x = xy
3) x + y = xy
4) xy = x/y
```

+1 vote

Given 2^x = 3^y =6

Taking log on all the sides we get

Log 2^x = Log 3^y = Log6

xLog2 = yLog3 = Log 6

x= Log6/Log2

y= Log6/Log3

We know that Log(ab) = Log a + Log b

therefore Log6 = Log 2 + Log 3

x+y = (Log 6/ Log 2) + (Log 6/Log 3) = Log 6*((Log 2 + Log 3)/Log 2 Log 3) = (Log 6*Log 6/ Log 2* Log 3) = xy

**x+y = xy**

0 votes

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