Question 1186981
<pre>
{{{7^a - 7^(a-5) = 117642sqrt(7)}}}

{{{7^a - 7^a*7^(-5) = 117642(7^("1/2"))}}}

Factor out 7<sup>a</sup>

{{{7^a*(1 - 7^(-5)) = 117642(7^("1/2"))}}}

Divide both sides by 7<sup>1/2</sup>

{{{(7^a*(1 - 7^(-5)))/7^("1/2") = 117642}}}

{{{(7^a/7^("1/2"))(1 - 7^(-5)) = 117642}}}

{{{7^(a-"1/2")(1 - 7^(-5)) = 117642}}}

{{{7^(a-"1/2")(1 - 1^""/7^5) = 117642}}}

{{{7^(a-"1/2")(1 - 1^""/117642) = 117642}}}

{{{7^(a-"1/2")(1 - 1/16807) = 117642}}}

{{{7^(a-"1/2")a(16807/16807 - 1/16807) = 117642}}}

{{{7^(a-"1/2")(16806/16807) = 117642}}}

Multiply through by 16807

{{{7^(a-"1/2")(16806) = 1977209094}}}

Divide both sides by 16806

{{{7^(a-"1/2")=117649}}}

Take logs (base 10) of both sides

{{{log(7^(a-"1/2"))=log(117649)}}}

{{{(a-1/2)*log(7)=5.07058824}}}

{{{a-1/2=5.07058824/log(7)}}}

{{{a-1/2=6}}}

{{{a=6+1/2}}}

{{{a=13/2}}}

Edwin</pre>