Question #5bb0e

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Answer 1 · 2017-09-20T21:13:24

k=2

in more detail:
$5^(k+1)=x$
$(5 * x) + x - 750 = 0$
$6 * x = 750$
$->x=125$
$5^(k+1)=125$
$->k=2$

Answer 2 · 2017-10-31T12:46:27

Taking to where you can take over

Just to make things a bit more strait forward:

Set $m=k-1$ then we have:

$5^(m+3)+5^m=750$

$5^m(5^3+1)=750$

$5^m=750/126$

taking logs

$mln(5)=ln(750)-ln(126)$

$m= (ln(750)-ln(126))/ln(5)$

Thus $k-1= (ln(750)-ln(126))/ln(5)$

I will let you do the rest.