Use natural logarithms to solve the equation. Round to the nearest thousandth. 7e^2x + 10 = 29

Mathematics

1 answer:

xxTIMURxx [149]2 years ago

6 0

Answer:

x ≈ 0.499

Step-by-step explanation:

The value of x can be found by undoing the operations done to it.

<h3>Solution</h3>

The operations done to the variable are ...

multiply it by 2
use that as the exponent with a base of e
multiply the result by 7
add 10

We undo these operations in reverse order:

7e^(2x) + 10 = 29 . . . . given

7e^(2x) = 19 . . . . . . . . . subtract 10

e^(2x) = 19/7 . . . . . . . . . divide by 7

2x = ln(19/7) . . . . . . . . take the natural logarithm

x = (ln(19/7))/2 . . . . . . divide by 2

The rounded result is ...

x ≈ 0.499

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