help me with logarithm please

[pullingmyhairout]

Hello, I am new here, and glad I found this website.

I need to solve this equation by isolating the natural logarithm and exponentiating both sides. Then I need to express the answer in terms of 'e'. I am completely lost.

6 + 6 ln x=11

Any help is greatly appreciated.

 

[soroban]

Hello, pullingmyhairout!

I need to solve this equation by isolating the natural logarithm and exponentiating both sides.
Then I need to express the answer in terms of 'e'.

\(\displaystyle \;\;\;6\,+\,6\cdot\ln x\:=\:11\)

Did you try following the directions?

We have: \(\displaystyle \;6\,+\,6\cdot\ln x\;=\;11\)

Isolate the log:
\(\displaystyle \;\;\;\)Subtract 6 from both sides: \(\displaystyle \:6\cdot\ln x\;=\;5\)
\(\displaystyle \;\;\;\)Divide both sides by 6: \(\displaystyle \;\ln x\;= \;\frac{5}{11}\)

Exponentiate both sides: \(\displaystyle \L\;e^{^{\ln x}}\;=\;e^{^{\frac{5}{11}}}\)

Since \(\displaystyle e^{^{\ln x}}\,=\,x\). we have: \(\displaystyle \L\:x\:=\:e^{^{\frac{5}{11}}}\)

 

[Denis]

x = e^(5/6)
First mistake this year, Soroban ? :shock:

 

[soroban]

x = e^(5/6)
First mistake this year, Soroban ?

Starting off the new year with a really stupid blunder . . . aargh!

 

[pullingmyhairout]

Thanks soroban and Denis