Question

Which of the following is the solution to the equation 25^2c = square root of 5^(4c + 14) ?

Answer 1

\[25^{2c}=\sqrt{5^{4c+14}}\]?

Answer 2

the 4c+14 is not in the square root

Answer 3

\[25^{2c}=\sqrt{5}(4c+14)\]?

Answer 4

so confused

Answer 5

\[25^{2c}=\sqrt{5}^{(4c+14)?}\]

Answer 6

yes

Answer 7

ok
\[25^{2c}=5^{2c+7}\]
make sense?

Answer 8

yes so far

Answer 9

\[(5^2)^{2c}=5^{2c+7}\]

Answer 10

allright

Answer 11

\[5^{4c}=5^{2c+7}\]
take log base 5 of both sides
\[\log_5(5^{4c})=\log_5(5^{2c+7})\\4c\log_5(5)=(2c+7)\log_5(5)\\4c*1=(2c+7)*1\\4c=2c+7\\2c=7\\c=\frac{7}{2}\]

Answer 12

Thank you :)

Answer 13

np