Solving Exponential and Logarithmic Equations Week7

Recall: When an exponential equation has the same base on each side, the exponents must be equal.

Solve each equation using a common base.

25 ^3x = 125 ^x+2

• x = 1

• x = 2

• x = 3

• x = 4

• none of the above

Recall: When an exponential equation has the same base on each side, the exponents must be equal.

Solve each equation using a common base.

0.001= 10^6x

• x = 1

• x = - ½

• x = - ⅓

• x = - ¼

• none of the above

Rewrite the equation 5 ^x = 12 using logarithms.

• log 12 = log 5 ^x

• log 12⁵ = log x⁵

• log 5¹² = log 5^x

• log 12^x = log 5

• none of the above

Tags

CCSS.HSF.BF.B.5

What is the solution to 2 ^3x = 7 ^x+1 ?

• (log2) / (2log3 – log 7)

• (log7) / (7log2 – log 3)

• (log7) / (2log3 – log 7)

• (log7) / (3log2 – log 7)

• none of the above

Solve each equation: log₅ (x² – 45) = log₅ (4x)

• 9, 5

• 9, (-5 is extraneous)

• 5, (-9 is extraneous)

• 45, (- 4 is extraneous)

• none of the above

Solve each equation: ln ( -4x - 1) = ln (4x²)

• 1/2

• -1/2

• 2/3

• -2/3

• none of the above

Solve each of the following equations for x. (Remember, get the bases to match and use the one to one property to solve.) 16 ^2x+3 = 8 ^x+2

• x = 5/8

• x = 5/18

• x = 8/5

• x = 18/5

• none of the above

Solve each of the following equations for x. (Remember, get the bases to match and use the one to one property to solve.)

9 ^x+2 = 27 ^x-5

• 17

• 18

• 19

• 20

• none of the above

Solve each of the following equations for x. (Remember, get the bases to match and use the one to one property to solve.)

(1/2) ^x-4 = 4 ^2x-3

• 4

• 3

• 2

• 1

• none of the above

Solve each of the following equations for x. (Remember, get the bases to match and use the one to one property to solve.)

ln (2x – 3x) = ln 11

• x = 5

• x = 6

• x = 7

• x = 8

• none of the above