SOLUTION: Let 2^a = 6 and 2^b = 7. Using exponent rules, solve the equation in terms of a and/or b. 6^x = 64

Algebra ->  Exponents -> SOLUTION: Let 2^a = 6 and 2^b = 7. Using exponent rules, solve the equation in terms of a and/or b. 6^x = 64      Log On


   

Question 916442: Let 2^a = 6 and 2^b = 7. Using exponent rules, solve the equation in terms of a and/or b.
6^x = 64
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since 2^a = 6, we can replace 6 with 2^a

6^x = 64

(2^a)^x = 64

log( (2^a)^x ) = log( 64 )

x*log(2^a) = log(64)

x = log(64)/log(2^a)

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
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Thanks,

Jim