Logarithm and Exponential Equations

Rewrite in exponential form:
log (x) = ¼

• x^1/4 = 1
• 1^x =¼
• 10^1/4 = x
• 10^x = ¼

Tags

CCSS.HSF.BF.B.5

Write as a single logarithm

• log xyz³

• log (xy/z³)

• log x + log y + log z³

• log x³y³z³

Solve the equation.

• A
• B
• C
• D

What is the value of ln(e⁷)

• 2.718...
• 1
• 7
• Does not exist

Tags

CCSS.HSF.BF.B.5

 $\log_2\sqrt{3x^2}$  

Expand the following logarithmic expression.

•  $\frac{1}{2}\log_23+\log_2x$  

•  $\frac{1}{2}\log\ 3\ +\frac{1}{2}\log\ x$  

•  $-2\ \log_2\ 3\ -\log_2x$  

•  $2^3=x^2$  

Solve 3³ = 3^{4x + 2}

• x = ¼
• x = -¼
• x = ½
• x = -½

Solve for x:
5^2x = 5^-x

• 0
• -6
• 8
• 1

Solve: 2^x = 4^x+1

• x = -2
• x = 2
• x = -3
• x = 3

Sovle for x:
5^{-3x - 1} = 25

• x = -1
• x = -4
• x = -3
• x = 1

Evaluate the log by thinking " 3 to what power is 1/9" so

log₃(1/9) =

• 1/2

• 2

• -2

• 3