What exponent should I raise $26$ to in order to equal $2^{76}$?

Question

I want to figure out how long an all-caps password needs to be to equal $2^{76}$ bits of security.

I would type this into Wolfram Alpha, but I'm not sure what function to use or if it can compute (what I think is) a number field sieve.

Any assistance in computing this would be appreciated.

Answer 1

$$2^{76} = 26^x$$

$\ln$ both sides:

$$76 \ln 2 = x \ln 26 \implies x = \frac{76 \ln 2}{\ln 26} \approx 16$$

Answer 2

Hint : apply log to $26^x=2^{76}$

Answer 3

Use this link to post into Wolfram Alpha: http://www.wolframalpha.com/input/?i=Log%5B26%2C2%5E76%5D

Answer 4

Wolfram understands natural language, sort of.

So type

"solve 26^x = 2^76 over the reals" and you get your answer...