Question 1186981
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find the value of a if 7^a - 7^(a-5) = 117642 sqrt 7
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<pre>
The starting equation

    {{{7^a - 7^(a-5)}}} = {{{117642*sqrt(7)}}}


is EQUIVALENT to

    {{{7^(a-5)*(7^5-1)}}} = {{{117642*sqrt(7)}}},

    {{{7^(a-5)*16806}}}   = {{{117642*sqrt(7)}}},


and then, canceling the common factor  16806 in both sides

    {{{7^(a-5)}}} = {{{7*sqrt(7)}}}.


It implies  

    a - 5 = {{{3/2}}},


hence

    a = 5 + {{{3/2}}} = 6 {{{1/2}}} = 6.5.    <U>ANSWER</U>
</pre>

Solved.