Question 278941
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{{{12e^(8t)-e=8e^(8t)}}}

{{{12e^(8t)-8e^(8t)=e}}}

{{{4e^(8t)=e}}}


Divide both sides by e

{{{(4e^(8t))/e=e/e}}}

Notice that e is raised to the first power on the
left bottom, so you subtract exponents:

{{{(4e^(8t))/e^1=1}}}

{{{4e*(8t-1)=1}}}

Take natural logs of both sides:

{{{ln(4e*(8t-1))=ln(1)}}}

Use laws of logarithms:

{{{ln(4)+ln(e^(8t-1))=0}}}

Use another law of logarithms:

{{{ln(4)+(8t-1)=0}}}

{{{ln(4)+8t-1=0}}}

{{{8t=1-ln(4)}}}

Divide both sides by 8

{{{t=(1-ln(4))/8}}} or about -.0482867951

Edwin</pre>