Question

1) Log(2)8^x= - 3 2) 5e^0.2x=7 The 2 in parenthesis is the base. What's the value of x?

Answer 1

I found:
`x_1=-1`
`x_2=1.6824`

Explanation:

1) you can write (definition of log):
`log_2(8^x)=-3`
`8^x=2^-3`
`8^x=1/2^3=1/8`
`8^x=8^-1`
so taking the `log_8` on both sides;
`x=-1`

2)`5e^(0.2x)=7`
`e^(0.2x)=7/5` taking the `ln` on both sides:
`0.2x=ln(7/5)`
`x=1.6824`