Question

please help me with this question 200(2)^t/3=500(1/4)^t/5

Answer 1

\[200 \cdot 2^\frac{t}{3}=500 \cdot (\frac{1}{4})^\frac{t}{5}\]?

Answer 2

\[200 \cdot 2^{\frac{t}{3}}=500(2^{-2})^\frac{t}{5} \\ 200 \cdot 2^\frac{t}{3}=500(2^\frac{-2t}{5}) \\ 200(2^\frac{t}{3})-500(2^{\frac{-2t}{5}})=0 \\ 100 \cdot 2^{\frac{-2t}{5}}(2 ^{\frac{11t}{15}}-5)=0 \]
check my math

Answer 3

also this should make it easier for you to solve for t :)

Answer 4

how about the log on both sides ?

Answer 5

T=30000/7997

Answer 6

@Tin2015

Answer 7

you just need to solve:
\[2^{\frac{11t}{15}}=5\]
yes do ln( ) on both sides

Answer 8

Ok thank you freckles :)