A2: 7.7 Solving Base e and Natural Logarithms

The natural logarithm has what base?

• 10
• 0
• e
• -e

Expand ln xy²z³

• 6(lnx + lny - lnz)
• lnx + 2lny - 3lnz
• lnx + (1/2)lny + (1/3)lnz
• lnx + 2lny + 3lnz

Rewrite in exponential form:
ln(2) = x

• 2^x = 10
• 10² = x
• e^x = 2
• e² = x

Write this Natural Logarithmic function into Base "e" form:

ln15 = 2.71

• log_e 15 = 2.71

• e^2.71 = 15

• e¹⁵ = 2.71

• e = 15

Solve the following equation.  Round your solution to two decimal places.
4 - 3 ln(2x + 10) = 12

• x = 2.20
• x = 1.68
• x = -5.00
• x = -4.97

Solve the following equation.  Round your answer to two decimal places;
5 ln(x) = 7

• x = 4.06
• x = 2.04
• No solution
• None of the above

Solve for x:
e^x=7

• x=ln7
• x=ln⁷
• x=7^ln
• No solution

What is the value of ln(e⁷)

• 2.718...
• 1
• 7
• Does not exist

Rewrite in exponential form:
ln(2) = x

• 2^x = 10
• 10² = x
• e^x = 2
• e² = x

Solve for x:
5 e^6x+3 = 0.1

• -1.152
• 0.232
• -3.077
• -0.854