MHB Is This Use of Logarithmic Rules Correct in Solving for x?

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The discussion focuses on verifying the correctness of logarithmic rules used to solve the equation y = ln(x) + 1 for x. The initial solution presented simplifies to x = e^(y-1), which is confirmed as correct. An alternative method using logarithmic properties also leads to the same conclusion, demonstrating the validity of both approaches. Participants express satisfaction with the accuracy of the methods used. The thread highlights the importance of understanding logarithmic rules in solving equations effectively.
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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:
$$y-1=ln(x)$$
$$\therefore \text {by definition}\ x=e^{y-1}$$

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

Both methods look spot on to me! :D
 
Re: basic question regarding log rules

MarkFL said:
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)
 
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