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

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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)

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}