Find `x` given `100^(x-2) = 1000^x`. (2 marks)
Functions, 2ADV F1 SM-Bank 53
- If `1/(root3(7+pi)) = (7+pi)^x`, find `x`. (1 mark)
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- Calculate the value of `1/(root3(7+pi))` to 3 significant figures. (1 mark)
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L&E, 2ADV E1 2019 HSC 15a
Solve `e^(2 ln x) = x + 6` (2 marks)
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L&E, 2ADV E1 2019 HSC 3 MC
What is the value of `p` so that `(a^2a^(-3))/sqrt a = a^p`?
- `-3`
- `-3/2`
- `-1/2`
- `12`
L&E, 2ADV E1 SM-Bank 8
Solve the equation `3^(-4x) = 9^(6-x)` for `x.` (2 marks)
L&E, 2ADV E1 SM-Bank 10
Solve the equation `2^(3x-3) = 8^(2-x)` for `x`. (2 marks)
L&E, 2ADV E1 SM-Bank 11 MC
Solve the equation `e^(4x) - 5e^(2x) + 4 = 0` for `x`
(A) `x= 1, 4`
(B) `x= – 4, – 1`
(C) `x= 0, log_e 2`
(D) `x= – log_e 2, 0, log_e 2 `
L&E, 2ADV E1 2004 HSC 6a
Solve the following equation for `x`:
`e^(2x) + 3e^x − 10 = 0`. (2 marks)
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L&E, 2ADV E1 2007 HSC 6a
Solve the following equation for `x`:
`2e^(2x) - e^x = 0`. (2 marks)
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L&E, 2ADV E1 2015 HSC 8 MC
L&E, 2ADV E1 2006 HSC 1a
Evaluate `e^(−0.5)` correct to three decimal places. (2 marks)
L&E, 2ADV E1 2010 HSC 4d
Let `f(x)=1+e^x`.
Show that `f(x)xxf(–x)=f(x)+f(–x)`. (2 marks)
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L&E, 2ADV E1 2011 HSC 1c
Solve `2^(2x+1)=32`. (2 marks)