Question

If `x+log_(15)(1+3^(x))=xlog_(15)5+log_(15)12`, where x is an integer, then what is x equal to?
A. `-3`
B. 2
C. 1
D. 3

Answer 1

Correct Answer - C
`x+log_(15)(1+3^(x))=x log_(15)5+log_(15)12`
`impliesx.log_(15)15+log_(15)(1+3^(x))=xlog_(15)5+log_(15)12" "(because log_(15)15=1)`
`implieslog_(15)15^(x)+log_(15)(1+3^(x))=log_(15)5^(x)+log_(15)12`
`=log_(15)15^(x)(1+3^(x))=log_(15)(5^(x)xx12)" "(because loga+logb=logab)`
`implies15^(x)(1+3^(x))=5^(x)xx12`
`implies3^(x)(1+3^(x))=12`
`3^(x)+3^(2x)=12`.
x=1 satisfies the above equation.