Question

How do you condense `1/2(log_4(x+1)+2log_4(x-1))+6log_4x`?

Answer 1

Let `E = 1/2[log_4(x+1) + 2log_4(x-1)] + 6log_4x` represent your expression (just so then I don't have to rewrite it so often!). Using the logarithm's identities:

`E = 1/2[log_4(x+1)+ log_4(x-1)^2] + log_4x^6`;

`E = 1/2log_4[(x+1)(x-1)^2] + log_4x^6`;

`E = log_4[(x+1)^(1/2)(x-1)] + log_4x^6`;

`E = log_4[(x+1)^(1/2)(x-1)x^6]`.