MHB Solving the Equation: Two Answers?

[siyanor]

I have an equation which answered it in two ways,which one is correct ?View attachment 163

 

[SuperSonic4]

I have an equation which answered it in two ways,which one is correct ?
https://www.physicsforums.com/attachments/163

The first method is not correct because ln(7.3) has simply disappeared.

The second method is correct but the rounded answer is not correct. $ x = \frac{1}{2}\left(\frac{\ln(10)}{\ln(7.3)}-1\right) \approx 0.0792 $

 

[checkitagain]

I have an equation which answered it in two ways,which one is correct ?https://www.physicsforums.com/attachments/163

7.3^{2x + 1} \ = \ 10

siyanor,

(regarding the correct process of method #2),
because you have 10 on one side at that point,
that lends itself to taking log (base 10) of each
side:

\log_{10}7.3^{2x + 1} \ =\log_{10}10(2x + 1)\log(7.3) \ = \ 12x + 1 \ = \ \dfrac{1}{log(7.3)}And continue . . .