Question 156857
<font size = 6 color = "red"><b>Edwin's solution:
<pre><font size = 4 color = "indigo"><b>
You don't need to go into logs in base 12, just use 
natural logs:

{{{12^(m+5)=17}}}

Take natural logs of both sides

{{{ln(12^(m+5))=ln(17)}}}

Use the rule {{{ln(A^C)=C*ln(A)}}} on the left:

{{{(m+5)ln(12)=ln(17)}}}

Divide both sides by {{{ln(12)}}}

{{{m+5=ln(17)/ln(12)}}}

Add -5 to both sides

{{{m=ln(17)/ln(12)-5}}} or

{{{m=-3.859831075}}}

Edwin</pre>