Make Up Log & Exponentials Test

Solve the following for 'x';
log₆(3x - 2) = log₆(5x - 8)

• x = 3
• x = 2
• x = -1
• No Solution

Use multiple log properties to write as a single log:
log₂x -  5log₂y

• log₂(x/y⁵)
• log₂(xy⁵)
• log₂(x/y)⁵
• log₂(x/5y)

Solve for x:  log₆x + log₆(x-5) = 2

• √7
• 9
• 4
• none of these

Evaluate log₅  20 to the third decimal place

• 0.537
• 2.996
• 1.301
• 1.861

Write the exponential equation as a logarithm
6³=216

• log₆(3) = 216
• log₃(6) = 216
• log₆(216)=3
• log₂₁₆(6)=3

Solve for x.
e^x+6 + 5 = 1

• -4.614
• -4.236
• No Solution
• -0.334

log(x+6) = 1

• 4
• 4.222
• -5
• -9.550

Rewrite the expression in logarithmic form.

 $w^3=40$  

•  $\log_w40=3$  

•  $\log_{40}w=3$  

•  $\log_340=w$  

•  $\log_w3=40$  

Rewrite the expression in exponential form.

 $\ln\left(x+2\right)=5$  

•  $e^{\left(x+2\right)}=5$  

•  $5^e=x+2$  

•  $\left(x+2\right)^e=5$  

•  $e^5=x+2$  

Condense the expression into a single logarithm.

 $\log_73+2\log_7x$  

•  $\log_7\left(3x^2\right)$  

•  $2\log_7\left(3x\right)$  

•  $\log_7\left(6x\right)$  

•  $\log_7\left(9x^2\right)$