Prove: `log_b1 = 0`

Prove: log_b b = 1

Prove: log_b b^x=x

Write the following using powers log_5 1 = 0

Show that a^(0)= 1" so " log_(a)1= 0

Prove that log_(a)xy=log_(a)x+log_(a)y.

Write the following using powers log_8 0.125 = -1

Prove the following int_(0)^(pi/4)2tan^(3)xdx=1-log2

If int(log 2)^(x) (dy)/(sqrt(e^(y) -1)) = (pi)/(6) , prove that x = log 4

If x^2 + y^2 = 10xy , prove that 2 log (x + y) = log x + log y + 2 log 2 + log 3 .

We can write log"" x/y = log (x.y^(-1 )) Can you prove that log"" x/y = log x - logy using product and power rules.