Question

Which of the following is the solution to the equation 25^(2c) = √5^(4c – 10) ?

c = 4

c = – 5 / 2

c = 7

c = 7 / 2 Which of the following is the solution to the equation 25^(2c) = √5^(4c – 10) ?

c = 4

c = – 5 / 2

c = 7

c = 7 / 2 @Mathematics

Answer 1

\[y=25^{2c}<=>\ln y=2c \ln 25\]
\[y=\sqrt{5}^{(4c-10)} <=> \ln y=(4c-10)\ln (\sqrt{5})\]
So \[2c \ln 25=(4c-10)\ln (\sqrt{5})\]
\[2c \ln (5^2)=(4c-10)\ln (5^{0.5})\]
\[4c\ln5=\frac{1}{2}(4c-10)\ln5\]
\[4c=2c-5\]
\[c=-\frac{5}{2}\]