calculus

[jlbc]

Ted, I have no clue how to even start...

Suppose log(b)2 = a and log(b)3 = c, find the following: log(b)1728b = ?. Thank you.

 

[BigGlenntheHeavy]

$\displaystyle Given: \ log_b 2 \ = \ a \ and \ log_b 3 \ = \ c, \ find \ log_b (1728b).$

$\displaystyle log_b(1728b) \ = \ log_b[(2^6)(3^3)(b)] \ = \ 6log_b 2+3log_b 3+log_b b \ = \ 6a+3c+1.$

$\displaystyle Factor, \ factor, \ factor, \ (FTA).$