What is the approximate solution of 7^x=3^x+1?

Question

I've tried to use log(10) to bring the exponents to the front but I keep ending up canceling out my variables. 

Answer 1

7^x=3^(x+1)

take log of both sides

log(7^x)=log(3^[x+1])

xlog(7)=(x+1)(log[3])

xlog(7)=xlog(3)+log(3)

xlog(7)-xlog(3)=log(3)

x[log(7)-log(3)]=log(3)

x[log(7/3)]=log(3)

x[log(2.333333333)=log(3)

x(0.36797678529)=0.47712125474

x=0.47712125474/0.36797678529

x=1.296606942

Answer 2

7^x=3^(x+1)   take log of both sides

 

xlog(7)=(x+1)*log(3) solve for x

 

x=-log(3)/(log(3)-log(7))

 

Jim