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 January 6th, 2010, 02:27 PM #1 Newbie   Joined: Jan 2010 Posts: 1 Thanks: 0 Help on Math test So basically I got a math test back and it was about logs, i think some of the questions were marked wrong so im here to clerify. 1st question is simply this expression -4^-1/2 all over (-^-2/3 2nd question is evaluate the exponential function y = 10^x for the given value of x x = -2/3 3rd question is expand: log with a base of 3[xa^2 over z^2] 4th question is Solve for y in terms of x: logy = logx-2log5 + 2 5th question is solve for x: Log with a base of 4 Sinx = -0.5 6th question is solve for x: 2e^(3x + 1)= 109.2 7th question is Solve for x: Inx-In1/3 = 1 Final question is Solve for x: log with a base of 8(x+2) = 2-log with a base of 8 2 Hope thats not too confusing
January 6th, 2010, 08:19 PM   #2
Math Team

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Re: Help on Math test

Here are a few of them . . .

Quote:
 $\text{{4. Solve for }y:\;\;\log(y) \:=\: \log(x)\,-\,2\log(5) \,+\, 2$

$\text{We have: }\;\log(y) \:=\:\log(x) \,-\,\log(5^2)\, + \,\log(10^2)$

[color=beige]. . . . . . . . .[/color]$\log(y)\:= \; \log(x) \,-\, \log(25) \,+\, \log(100)$

[color=beige]. . . . . . . . .[/color]$\log(y) \:=\:\log\left(\frac{x\,\cdot\,100}{25}\right)$

[color=beige]. . . . . . . . .[/color]$\log(y) \:=\:\log(4x)$

$\text{Therefore: }\qquad\qquad \qquad\qquad y \;=\;4x$

Quote:
 $\text{6. Solve for }x:\;\;\ln x\,-\, \ln\left(\frac{1}{3}\right) \:=\:1$

$\text{We have: }\;\ln\left(\frac{x}{\frac{1}{3}}\right) \:=\:1 \qquad\qquad\Rightarrow\qquad\qquad \ln(3x) \:=\:1$

$\text{Exponentiate: }\;3x \:=\:e^{^1} \qquad\qquad\Rightarrow\qquad\qquad x \:=\:\frac{e}{3}$

Quote:
 $\text{7. Solve for }x:\;\;\log_8(x\,+\,2) \;=\; 2\log_8(2)$

$\text{We have: }\;\log_8(x\,+\,2) \;=\;\log_8(2^2)$

[color=beige]. . . . . . . . [/color]$\log_8(x\,+\,2) \;=\;\log_8(4)$

$\text{Exponentiate: }\qquad x\,+\,2 \;=\;4 \qquad\qquad \Rightarrow\qquad\qquad x \:=\:2$

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