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Basic question regarding log rules

DeusAbscondus

Active member
Jun 30, 2012
176
Would some kind soul please look over the following and check that use of the log rules, thought roundabout, is nonetheless correct?
(thx kindly: I'm revising stuff I tried to cram last year)

The set question:

Solve for x:

$$y=ln(x)+1$$

Answer given in text:
$$y-1=ln(x)$$
$$\therefore \text {by definition}\ x=e^{y-1}$$

$\text{My attempt, using log laws: }$
$$y=ln(x)+1$$
$$\Rightarrow y=ln(x)+ln(e)$$
$$\Rightarrow y=ln(ex)$$
$$\therefore \text{ by definition} \ e^{y}=ex $$
$$\Rightarrow x=\frac{e^y}{e}$$
$$\therefore x=e^{y-1}$$
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: basic question regarding log rules

Both methods look spot on to me! :D
 

DeusAbscondus

Active member
Jun 30, 2012
176
Re: basic question regarding log rules

Both methods look spot on to me! :D
Thanks kindly Mark.
I like the new look in the new photo: real fun party-guy!(Rofl)