Question 701772
<pre>
The above tutor thought you meant

3<sup>x</sup> + 1 = 100

because you didn't put the exponent in parentheses, which
you should have done.  However I and the first tutor above
knew that by the time you get to logarithms, no teacher would
bother giving you a problem that would waste time to test you
on such a simple basic thing like whether you can subtract 1  
from both sides.  That's too elementary a thing to be testing 
someone already studying logarithms. So I assumed you meant

3<sup>x+1</sup> = 100

You can also do it using natural logs instead of logs base 10

3<sup>x+1</sup> = 100

ln(3<sup>x+1</sup>) = ln(100)

(x+1)ln(3) = ln(100)

{{{(  (x+1)ln(3)  )/ln(3)}}} = {{{ln(100)/ln(3)}}}

{{{  (x+1)cross(ln(3))/cross(ln(3))}}} = {{{ln(100)/ln(3)}}}

x+1 = {{{4.605170186/1.098612289}}}

x+1 = 4.19180655

  x = 3.19180655

Edwin</pre>