Question

Find the solution of the exponential equation, correct to four decimal places.
5^x=4^(x+2)

Answer 1

\(\large 5^x=4^{x+2} \)
\(\large 5^x=4^x \cdot 4^2 \)
\(\large \frac{5^x}{4^x}= 4^2 \)
\(\large (\frac{5}{4})^x= 2^4 \)
\(\large x\cdot ln(\frac{5}{4})=4ln2 \)
\(\large x\cdot (ln5-ln4)=4ln2 \)
\(\large x\cdot (ln5-2ln2)=4ln2 \)
\(\large x=\frac{4ln2}{ln5-2ln2} \)

Answer 2

now just use your calculator....

Answer 3

THANK YOU SO MUCH!!!!!!! I WOULD HAVE NEVER THOUGHT OF DOING THAT!!

Answer 4

yw...
i don't have a calculator but wolfram will do....
http://www.wolframalpha.com/input/?i=solve+5%5Ex%3D4%5E%28x%2B2%29