Question

Question #3a27d

Answer 1

Please see the explanation

Explanation:

Given: `77=33^x`

Use the natural logarithm on both sides:

`ln(77)=ln(33^x)`

All logarithms have the property `ln(a^c) = (c)ln(a)`; we shall use the property on the right side:

`ln(77)=(x)ln(33)`

Divide both sides by `ln(33)`:

`x = ln(77)/ln(33)`

The following is an approximation rounded to seven decimal places:

`x ~~ 1.2423269`

Given: `0.77=ln(y)`

Flip the equation:

`ln(y) = 0.77`

Make both sides an exponent of the exponential function:

`e^(ln(y)) = e^0.77`

We do this, because the exponential function and the natural logarithm cancel each other, thereby, leaving only y on the left:

`y = e^0.77`

The following is an approximation rounded to seven decimal places:

`y ~~ 2.1597663`