Question

Find x:
2(5)^x=3^(x+1)

I'm not sure what to do with the 2. I think I need to write the equation as log5^2x=log3^(x+1), but I don't know.

Thanks

Answer 1

If it is supposed to be

2 * 5^x = 3^(x+1)

then just take logs as usual:

log(2) + xlog(5) = (x+1)log(3)
log2 + xlog5 = xlog3 + log3
x(log5-log3) = log3-log2
x = (log3-log2)/(log5-log3)
or, if you prefer,
x = log(3/2)/log(5/3)

Answer 2

Thanks. That really helped!