The value of x in the given logarithmic equation is (ln8 – 6)/3. The correct option is A.
What are Natural logs?
The natural logarithm or log of a number is defined as its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459.
The value of x in the logarithmic equation [tex]e^{3x+6} = 8[/tex] can be found as shown below.
[tex]e^{3x+6}=8[/tex]
Taking the antilog,
3x + 6 = ln 8
Subtracting 6 from both sides of the equation,
3x – 6 = ln8 – 6
Dividing both sides of the equation by 3,
x = (ln8 – 6)/3
Hence, the value of x in the given logarithmic equation is (ln8 – 6)/3.
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