SOLUTION: Solve the exponential equation. Express the solution set in terms of natural logarithms. 4^x+4 = 5^2x+5 Answers: A) {7 ln 5 - 5 ln 4} B) {5 ln 5 - 4 ln 4/ln 4

SOLUTION: Solve the exponential equation. Express the solution set in terms of natural logarithms. 4^x+4 = 5^2x+5 Answers: A) {7 ln 5 - 5 ln 4} B) {5 ln 5 - 4 ln 4/ln 4 - 2 ln 5}

Question 824581: Solve the exponential equation. Express the solution set in terms of natural logarithms.
4^x+4 = 5^2x+5
Answers:
A) {7 ln 5 - 5 ln 4}
B) {5 ln 5 - 4 ln 4/ln 4 - 2 ln 5}
C) {ln[5^5/4^4 - 4/5^2]}
D) {ln 5 - ln 4}
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
4^(x+4) = 5^(2x+5)
take ln of each side
ln(4^(x+4) ) = ln( 5^(2x+5) )
(x+4)ln(4) = (2x+5)ln(5)
ln(4)*x + 4ln(4) = ln(5)*2x + 5ln(5)
subtract 4ln(4) from each side
ln(4)*x = ln(5)*2x + 5ln(5)-4ln(4)
subtract ln(5)*2x from each side
ln(4)*x - ln(5)*2x = 5ln(5)-4ln(4)
ln(4)*x - ln(5^2)*x = ln(5^5)-ln(4^4)
(ln(4) - ln(5^2))*x = ln(5^5)-ln(4^4)
divide each side by (ln(4) - ln(5^2))
x =
This can be rewritten as
x =
which is the same as B) assuming
B) (5 ln 5 - 4 ln 4)/(ln 4 - 2 ln 5)
RELATED QUESTIONS
Solve the exponential equation. Express the solution set in terms of natural logarithms. (answered by stanbon)

solve the exponential equation, express the solution set in terms of natural logarithms: (answered by lwsshak3)

Express the solution set in terms of natural logarithms.... (answered by Fombitz)

im so lost with this one... Solve the exponential equation. express the solution set... (answered by Alan3354,jsmallt9)

Express the solution set in terms of natural logarithms.... (answered by Fombitz)

Solve the exponential equation. Express the solution set in terms of natural logarithms. (answered by Alan3354,stanbon)

Solve the exponential equation. Express the solution set in terms of natural logarithms. (answered by user_dude2008)

solve the exponential equation. Express the solution set in terms of natural logarithms. (answered by Alan3354)

solve the expontel equation. espress the soloution set in terms of natural logs... (answered by Edwin McCravy)