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In Mathematics / High School | 2014-11-14

Solve the equation. Write the answer in terms of the natural logarithm.

\[ e^{9x+8} = 14 \]

Asked by williamslashay6

Answer (3)

e 9 x + 8 = 14 9 x + 8 = ln 14 9 x = ln 14 − 8 x = 9 1 ​ ( ln 14 − 8 )

Answered by konrad509 | 2024-06-10

x = 9 l n ( 14 ) − 8 ​ in terms of natural logarithm for the equation e 9 x + 8 = 14 .
The equation consists of two expressions combined with an eqaul to symbol.
Given the following equation :
e 9 x + 8 = 14
To express it in terms of natural logarithm, take natural logarithm on both sides of the equation as follows:
l n ( e 9 x + 8 ) = l n ( 14 )
natural logarithm is an inverse operation to e,
9 x + 8 = l n ( 14 ) 9 x = l n ( 14 ) − 8 x = 9 l n ( 14 ) − 8 ​
Thus, x = 9 l n ( 14 ) − 8 ​ for the equation e 9 x + 8 = 14 .
Learn more about equation , here:
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Answered by mahendravt | 2024-06-17

The solution to the equation e 9 x + 8 = 14 is x = 9 ln ( 14 ) − 8 ​ . We find this by taking the natural logarithm of both sides and isolating x . This process demonstrates the use of natural logarithms to solve exponential equations.
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Answered by mahendravt | 2024-12-26

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