Exponential and Logarithmic Equations

[RB67]

Hi. I'm stuck on a problem because I missed yesterday's lecture. Hopefully someone here can guide me through this problem.

Instructions: Solve each equation: If an answer is not exact, give the answer to four decimal places.

Problem: \(\displaystyle \L\, 7^{(x^2)}\, =\, 10\)

My work so far:

. . .\(\displaystyle \L x^2 \, \log{(7)}\, =\, \log{(10)}\)

. . .\(\displaystyle \L \frac{x^2\, \log{(7)}}{\log{(7)}}\, =\, \frac{\log{(10)}}{\log{(7)}}\)

. . .\(\displaystyle \L x^2\, =\, \frac{\log{(10)}}{\log{(7)}}\)

But then what does x^2 equal?

Thanks.
_______________________
Edited by stapel -- Reason for edit: replacing graphic with text.

 

[Random]

Keep going!


x^2 = log(10)/log(7)

Just like you have. Keep solving.

Take the square root of both sides, and there is your answer.

 

[RB67]

log(3)= 0.477121255

Then I take the square root of that and I get 0.690739643 but the answer in teh back of the book is +-1.0878.

Where did I go wrong?

 

[galactus]

I can't believe I just done that.

\(\displaystyle \L\\x=\pm\sqrt{\frac{log(10)}{log(7)}}\)

forget the log(3). That was me having a major brain fart.

 

[RB67]

Haha. I just figured that out, well my sister helped me out. Thanks for the help. Will be back later if I get stuck again.