Question

Find the value of K in the following equations: (a) (7)^-1x (7)^3k+2 = (7)^15+ (7)^8
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Answer 1

Answer:

$\mathrm{\left(7\right)^{-1}\left(7\right)^3k+2=\left(7\right)^{15}+\left(7\right)^8\quad :\quad k=\frac{7^{15}+5764799}{49}}$

Step-by-step explanation:

$\left(7\right)^{-1}\left(7\right)^3k+2=\left(7\right)^{15}+\left(7\right)^8$

$\mathrm{49k+2=7^{15}+5764801}$

$\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}$

$\mathrm{49k+2-2=7^{15}+5764801-2}$

$\mathrm{49k=7^{15}+5764799}$

$\mathrm{Divide\:both\:sides\:by\:}49$

$\mathrm{\frac{49k}{49}=\frac{7^{15}}{49}+\frac{5764799}{49}}$

$\mathrm{k=\frac{7^{15}+5764799}{49}}$