Question

Eˣ=7is equivalent to the logarithmic equation:

A) ln(7)=x
B) 7=ln(x)
C) x=log ₇ (e)
D) log ₑ(7)=x

Answer 1

`\Large \textsf{Read below}`

Step-by-step explanation:

`\Large \text{$ \sf e^x = 7$}`

`\Large \text{$ \sf ln\:e^x = ln\:7$}`

`\Large \text{$ \sf x = ln\:7$}`

`\Large \boxed{\boxed{\text{$ \sf ln\:7 = x$}}}`

Answer 2

eˣ=7 is equivalent to the logarithmic equation ln(7)=x because the natural logarithm (ln) is the power to which e must be raised to result in 7.

Step-by-step explanation:

The equation ex = 7 is equivalent to the logarithmic equation that solves for x in terms of the natural logarithm. The natural logarithm (ln) of a number is the power to which e must be raised to equal the number. The correct transformation of the exponential equation into a logarithmic equation is ln(7) = x, reflecting that x is the exponent to which e must be raised to get 7.

To convert an exponential equation to its logarithmic form, we use the property that if ab = c, then loga(c) = b. Applying this to our initial equation, we get loge(7) = x, which simplifies to ln(7) = x because the natural logarithm implies a base of e.