Answer:
x≈4
Step-by-step explanation:
We are given that
[tex]2^{x} \times 3^{x}=1296[/tex]
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
[tex]\log(2^{x} \times 3^{x})=\log 1296[/tex] ----------------(A)
We know that
[tex]\log (a\times b)=\log a + \log b[/tex]
Hence applying this law in (A)
[tex]\log(2^{x} \times 3^{x})=\log 2^{x} + \log 3^{x}[/tex]
[tex]\log 2^{x} + \log 3^{x} =\log 1296[/tex] --------------(B)
Another property of logarithm says
[tex]\log a^{m} = m\log a[/tex]
Applying this law in (B)
[tex]x\log 2 + x\log 3 = \log 1296[/tex]
taking x as GCF
[tex]x(\log 2 + \log 3)=\log 1296[/tex]
[tex]x \log (2\times 3)=\log 1296[/tex]
[tex]x \log 6= \log 1296[/tex]
Dividing both sides by \log 6[/tex]
[tex]x=\frac{\log 1296}{\log 6}[/tex]
using calculator
log 1296 = 3.1126
log 6 = 0.7781
[tex]x=\frac{3.1126}{0.7781}[/tex]
x≈4
