How do you solve \ln ( 2x + 2) = 1.6?

1 Answer
May 8, 2017

x = e^1.6/2 - 1

Explanation:

Firstly, identify that color(red)ln is called the natural logarithm.

This means it is a logarithm of a number N with a base e.

log_e N which can be expressed as ln_e N

Like log_10 N can be written as lg N, ln_e N can be written as ln N for short.

Therefore, ln(2x+2) = 1.6

Now, taking the exponential e for both sides, we get:

color(red)e^ln(2x+2) = color(red)e^1.6

Note: e^color(red)(lna)= color(red)a

:.e^color(red)ln(2x+2) = color(red)(2x+2)

Continuing,

color(red)e^ln(2x+2) = color(red)e^1.6

2x+2 = e^1.6

2x = e^1.6 - 2 Dividing both sides by 2,

x = e^1.6/2 - 1