Solve for t 45=6e^(12.77t)

Math
45=6e12.77t
Rewrite the equation as 6e12.77t=45.
6e12.77t=45
Divide each term by 6 and simplify.
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Divide each term in 6e12.77t=45 by 6.
6e12.77t6=456
Cancel the common factor of 6.
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Cancel the common factor.
6e12.77t6=456
Divide e12.77t by 1.
e12.77t=456
e12.77t=456
Cancel the common factor of 45 and 6.
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Factor 3 out of 45.
e12.77t=3(15)6
Cancel the common factors.
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Factor 3 out of 6.
e12.77t=3⋅153⋅2
Cancel the common factor.
e12.77t=3⋅153⋅2
Rewrite the expression.
e12.77t=152
e12.77t=152
e12.77t=152
e12.77t=152
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln(e12.77t)=ln(152)
Expand the left side.
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Expand ln(e12.77t) by moving 12.77t outside the logarithm.
12.77tln(e)=ln(152)
The natural logarithm of e is 1.
12.77t⋅1=ln(152)
Multiply 12.77 by 1.
12.77t=ln(152)
12.77t=ln(152)
Divide each term by 12.77 and simplify.
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Divide each term in 12.77t=ln(152) by 12.77.
12.77t12.77=ln(152)12.77
Cancel the common factor of 12.77.
t=ln(152)12.77
Simplify ln(152)12.77.
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Divide 15 by 2.
t=ln(7.5)12.77
Rewrite.
t=2.0149030212.77
Divide 2.01490302 by 12.77.
t=0.1577841
t=0.1577841
t=0.1577841
Solve for t 45=6e^(12.77t)

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