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Logarithm, SMB-024

Solve  `log_9 27=x`  for `x`.  (2 marks)

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`3/2`

Show Worked Solution
`log_9 27` `=x`  
`9^x` `=27\ \ text{(by log definition)}`  
`log_10 9^x` `=log_10 27`  
`x log_10 9` `=log_10 27`  
`x` `=(log_10 27)/(log_10 9)`  
  `=3/2`  

Filed Under: Logarithms Tagged With: num-title-ct-patha, smc-4243-05-Solve by log definition, smc-4243-70-Solve exponentials

Logarithm, SMB-023

Solve  `log_16 2=x`  for `x`.  (2 marks)

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`0.25`

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`log_16 2` `=x`  
`16^x` `=2`  
`log_10 16^x` `=log_10 2`  
`x log_10 16` `=log_10 2`  
`x` `=(log_10 2)/(log_10 16)`  
  `=0.25`  

Filed Under: Logarithms Tagged With: num-title-ct-patha, smc-4243-05-Solve by log definition, smc-4243-70-Solve exponentials

Logarithm, SMB-012

Solve the equation  `log_9 x=-3/2`.  (2 marks)

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`x = 1/27`

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`log_9 x` `=-3/2`  
`x` `=9^(-3/2)`  
  `=1/(sqrt9)^3`  
  `=1/27`  

Filed Under: Logarithms Tagged With: num-title-ct-patha, smc-4243-05-Solve by log definition

Logarithms, SMB-011

Solve the equation  `log_4 x=3/2`.  (2 marks)

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`x = 8`

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`log_4 x` `=3/2`  
`x` `=4^(3/2)`  
  `=8`  

Filed Under: Logarithms Tagged With: num-title-ct-patha, smc-4243-05-Solve by log definition

Logarithms, SMB-009

What is the solution to the equation  `log_3(a-1) = -2`?  (2 marks)

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`a=10/9`

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`log_3 (a-1)` `= -2`
`a-1` `= 3^{-2}`
`a` `=1/3^2+1`
  `= 10/9`

Filed Under: Logarithms Tagged With: num-title-ct-patha, smc-4243-05-Solve by log definition

Logarithms, SMB-008

What is the solution to the equation  `log_3 x = -1`?  (1 mark)

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`x=1/3`

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`log_3 x` `=-1`
`x` `=3^{-1}`
  `=1/3`

Filed Under: Logarithms Tagged With: num-title-ct-patha, smc-4243-05-Solve by log definition

L&E, 2ADV E1 2014 HSC 3 MC

What is the solution to the equation  `log_2(x-1) = 8`? 

  1. `4`
  2. `17`
  3. `65`
  4. `257`
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`D`

Show Worked Solution
`log_2 (x-1)` `= 8`
`x-1` `= 2^8`
`x` `= 257`

 
`=>  D`

Filed Under: Log/Index Laws and Equations (Adv-2027), Log/Index Laws and Equations (Y11), Log/Index laws and Other Equations, Logarithms Tagged With: Band 4, num-title-ct-patha, num-title-qs-hsc, smc-4243-05-Solve by log definition, smc-6455-40-Logs - Other, smc-963-40-Log - Other

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