Question

What is x and y if 2^x times 3^x is 1296

Answer 1

x≈4

Explanation:

We are given that

`2^(x) * 3^(x)=1296`

And we are asked to solve it for x

In order to do that we will use the properties of logarithm

Taking log on both hand sides

`\log(2^(x) * 3^(x))=\log 1296` ----------------(A)

We know that

`\log (a* b)=\log a + \log b`

Hence applying this law in (A)

`\log(2^(x) * 3^(x))=\log 2^(x) + \log 3^(x)`

`\log 2^(x) + \log 3^(x) =\log 1296` --------------(B)

Another property of logarithm says

`\log a^(m) = m\log a`

Applying this law in (B)

`x\log 2 + x\log 3 = \log 1296`

taking x as GCF

`x(\log 2 + \log 3)=\log 1296`

`x \log (2* 3)=\log 1296`

`x \log 6= \log 1296`

Dividing both sides by \log 6[/tex]

`x=(\log 1296)/(\log 6)`

using calculator

log 1296 = 3.1126

log 6 = 0.7781

`x=(3.1126)/(0.7781)`

x≈4