Question

Suppose `Log_b2=a` and `Log_b3=c`, how do you find `Log_b(72b)`?

Answer 1

`log_b 72b=2c+3a+1`

Explanation:

`log_b 2=a`
`log_b 3=c`
`log_b 72b=?`

`log_b 72b=log_b 3^2*2^3*b`

`log _x ( k*l*m)=log_x k+log_x l+ log _x m`

`log_b 72b=log_b 3^2+log _b 2^3+log _b b`

`log_b=3^2=2*log_b 3=2*c`
`log _b 2^3=3*log _b 2=3*a`
`lob_b b=1`

`log_b 72b=2c+3a+1`