Question 1148139
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Please think about when parentheses are needed when you type algebraic expressions.<br>
Clearly you mean 7^a-7^(a-5), which is {{{7^a-7^(a-5)}}}, instead of 7^a-7^a-5, which is {{{7^a-7^a-5}}}, which is just -5.<br>
On the left, factor out a common factor of 7^(a-5):<br>
{{{7^a-7^(a-5) = (7^(a-5))(7^5-1) = (7^(a-5))*16806}}}<br>
On the right, using the prime factorization of 117642 or any other method, determine that {{{117642*sqrt(7) = 7*16806*sqrt(7)}}}<br>
Then we have<br>
{{{(7^(a-5))*16806 = 7*16806*sqrt(7)}}}<br>
from which we can obtain<br>
{{{7^(a-5) = 7*sqrt(7) = 7^1.5}}}<br>
So<br>
{{{a-5 = 1.5}}}
{{{a = 1.5+5 = 6.5}}}<br>
ANSWER: a = 6.5, or 13/2<br>