Question 220562
These problems require that we know how to convert from exponential form to logarithmic form and vice versa. So we we need to know:<ul><li>{{{log(a, b) = c}}} in exponential form is: {{{a^c = b}}}</li><li>{{{a^b = c}}} in logarithmic form is: {{{log(a, c) = b}}}</li></ul>
We also need to understand that {{{ln(x)}}} is the common name for {{{log(e, (x))}}}<br>
Now we're ready to start:
1. {{{3e^(2x) = 28}}}
Whenever we solve for x we are trying to isolate x on one side of the equation. So we'll start by dividing by 3:
{{{e^(2x) = 28/3}}}
Now we need to get x out of the exponent. This is where we need to know that this is the time to convert ro logarithmic form:
{{{log(e, (28/3)) = 2x}}}
{{{ln(28/3) =  2x}}}
Now we can divide by 2:
{{{(ln(28/3))/2 =  x}}}
With a calculator we san simplify the left side:
{{{1.1167961107535471 = x}}}<br>
2. {{{2ln(x-5)=3.65
Divide by 2:
{{{ln((x-5))= 1.825}}}
Now we need to get x out of the argument of the logarithm. This is the time to convert to exponential form:
{{{e^1.825 = x-5}}}
Adding 5 to each side:
{{{e^1.825 + 5 = x}}}
With a calculator we can simplify the left side:
{{{11.2027950191048646 = x}}}