Question

How do you solve `log(4x)=log 5+log(x-1)`?

Answer 1

`color(blue)(x=5)`

Explanation:

By the laws of logarithms:

`log_a(b)+log_a(c)=log_a(bc)`

`log(4x)=log5+log(x-1)`

`log(4x)=log(5x-5)`

`:.`

`4x=5x-5`

`x=5`

Answer 2

`x=5`

Explanation:

`"using the "color(blue)"laws of logarithms"`

`•color(white)(x)logx+logy=log(xy)`

`•color(white)(x)logx=logyhArrx=y`

`rArrlog(4x)=log(5(x-1))`

`rArr5(x-1)=4x`

`rArr5x-5=4xrArrx=5`