Question

Question #808c0

Answer 1

For your first question, I'll have to explain what a log is. A log to a base `a`, i.e. `log_a(x)=b`, is another way of writing `a^x=b` or `a=root(x)(b)`. For example, `log_10(100)` will give us 2 because `sqrt(100)=10`, and `10^2=100`.

`a^(log_a(b))=b`. This can shown with `10^(log_10(100))`, `log_10(100)=2, 10^2=100`.

So, `log_5(4)` will tell you what number 5 has to be raised to the power of to get 4, in this case, 5 is raisedbto the power of that number, therefore giving 4.

For `log_3(2x+5)=2`, we know that the value for `x` will have to give us a number which when put into `2x+5` equals `3^2=9`

`9=2x+5`

`2x=4`

`x=4/2=2`