Mathematics: If 32^2c= 8^c+7, what is the value of c

If 32^2c= 8^c+7, what is the value of c - id32287822973, cicilee49

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vanessagomezcx

12.03.2022

$\bf 32^{2c}=8^{c+7}~~ \begin{cases} 32=2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^5\\ 8=2\cdot 2\cdot 2\\ \qquad 2^3 \end{cases}\implies (2^5)^{2c}=(2^3)^{c+7} \\\\\\ 2^{5(2c)}=2^{3(c+7)}\implies \stackrel{\textit{if the bases are the same, then so are the exponents}}{5(2c)=3(c+7)\implies 10c=3c+21} \\\\\\ 7c=21\implies c=\cfrac{21}{7}\implies c=3$

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If 32^2c= 8^c+7, what is the value of c

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