solve the exponential function 2^(2x+13)=3^(x-33) in terms of logs or round to the closest 4 decimal places

2^{2x + 13}  =  3^{x - 33}

Take the log of both sides:

log(2^{2x + 13}) =  log(3^{x - 33})

Since exponents come out as multipliers:

(2x + 13)log(2)  =  (x - 33)log(3)

Use the distributive property:

2xlog(2) + 13log(2)  =  xlog(3) - 33log(3)

Rearrange:

2xlog(2) - xlog(3)  =  -13log(2) - 33log(3)

Factor out the x:

x( 2log(2) - log(3) ) =  -13log(2) - 33log(3)

Divide:

x  =  [ -13log(2) - 33log(3) ] / [ 2log(2) - log(3) ]