Question #3a27d

1 Answer
Apr 8, 2017

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#