Question

What is the logarithmic form of the equation e5x = 1,298?

a
e = ln 12985x

b
5x = ln 1298e

c
log = 12985x

d
5x = ln 1298

Answer 1

Explanation:

The logarithmic form of an exponential equation is:

y = log(base b)(x)

if and only if

x = b^y

In this case, we have the exponential equation:

e^(5x) = 1,298

To write this in logarithmic form, we can take the natural logarithm (ln) of both sides:

ln(e^(5x)) = ln(1,298)

Using the rule that ln(e^y) = y, we can simplify the left-hand side:

5x = ln(1,298)

Finally, we can divide both sides by 5 to solve for x:

x = ln(1,298) / 5

Therefore, the logarithmic form of the equation e^(5x) = 1,298 is:

x = ln(1,298) / 5, or equivalently,

log(base e)(1,298) / 5