CK-12-Pre-Calculus Concepts

3.6. Exponential Equations http://www.ck12.org

log

(i

12

)

=− 0. 0145 ·d

log

(i

12

)

=− 0. 0145 · 10

log

(i

12

)

=− 0. 145

(i

12

)

=e−^0.^145

i= 12 ·e−^0.^145 ≈ 10. 380

3. First solve forex,

ex−e−x

3 =^14

ex−e−x= 42

e^2 x− 1 = 42 ex

(ex)^2 − 42 ex− 1 = 0

Letu=ex.

u^2 − 42 u− 1 = 0

u=−(−^42 )±

√(− 42 ) (^2) − 4 · 1 ·(− 1 )
2 · 1 =

42 ±√ 1768

2 ≈^42.^023796 ,−^0.^0237960

Note that the negative result is extraneous so you only proceed in solving forxfor one result.

ex≈ 42. 023796

x≈ln 42. 023796 ≈ 3. 738

Practice

Solve each equation forx. Round each answer to three decimal places.

1. 4x= 6


2. 5x= 2


3. 12^4 x= 1020


4. 7^3 x= 2400


5. 2x+^1 − 5 = 22


6. 5x+ 12 x= 5 x+ 7


7. 2x+^1 = 22 x+^3


8. 3x+^3 = 9 x+^1