Question

find the value of x,if 2 power x + 2 power (x+1) + 2 power (x+3) + 2 power (x+3) = 15*root32

Answer 1

2^x+2^(x+1)+2^(x+2)+2^(x+3)=15√32
2^x(1+2+2^2+2^3)=15√32
2^x(1+2+4+8)=15√32
2^x(15)=15√32
2^x=√32
taking log on both side
log2^x=log√32
x log 2=1/2 log 32    use logm^n=nlogm
xlog 2=1/2 log 2^5
xlog2=5/2log2
x=5/2