SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

  • Login
  • Get Help
  • About

L&E, 2ADV E1 EQ-Bank 6 MC

Given \(m\) and \(n\) are positive constants, which expression is equal to

\(\log _m x^5=n\)

  1. \(x=n^{\small{\dfrac{m}{5}}}\)
  2. \(x=m^{\small{\dfrac{n}{5}}}\)
  3. \(x=\dfrac{n^m}{5}\)
  4. \(x=\dfrac{m^n}{5}\)
Show Answers Only

\(\Rightarrow B\)

Show Worked Solution

\(\log _m x^5=n\)

\(\text{By definition:}\)

\(x^5=m^n\)

 \(x=\left(m^n\right)^{\small{\dfrac{1}{5}}}=m^{\small{\dfrac{n}{5}}}\)

\(\Rightarrow B\)

Filed Under: Log Laws and Equations (Y11), Log/Index Laws and Equations Tagged With: Band 4, smc-6455-35-Log Definition, smc-6455-40-Logs - Other, smc-963-50-Exponential Equation

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`
Show Answers Only

`D`

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

 
`=>  D`

Filed Under: Log Laws and Equations (Y11), Log/Index Laws and Equations, 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-6455-35-Log Definition, smc-6455-40-Logs - Other, smc-963-40-Log - Other

L&E, 2ADV E1 2009 HSC 1f

Solve the equation  `lnx=2`. Give you answer correct to four decimal places.   (2 marks) 

Show Answer Only

`7.3891`

Show Worked Solutions
MARKER’S COMMENT: Write answers to enough decimal places before rounding up.
`ln x` `=2`
`log_e x` `=2`
`x` `=e^2`
  `=7.38905…`
  `=7.3891\ \ text{(to 4 d.p.)}`

Filed Under: Log Laws and Equations (Y11), Log/Index Laws and Equations, Log/Index laws and Other Equations Tagged With: Band 4, smc-6455-35-Log Definition, smc-6455-40-Logs - Other, smc-6455-80-Significant Figures, smc-963-40-Log - Other

Copyright © 2014–2026 SmarterEd.com.au · Log in