solve 2^x = y for x — step-by-step solution

Let's solve in

ℝ

2^{x} = y

The logarithm being defined only for positive numbers, let's apply the ln function on both sides, provided that

y > 0

\ln (2^{x}) = \ln (y)

ⓘ On the real domain of the original expression, the base is strictly positive: the logarithm of the power is the exponent times the logarithm of the base:

\ln (2^{x})

x \cdot \ln (2)

x \cdot \ln (2) = \ln (y)

ⓘ Both sides are divided by

\ln (2)

Solution found:

x = \frac{\ln (y)}{\ln (2)}

Let's solve for y:

y > 0

Solution found:

y > 0

▶Solution:

{x = \frac{\ln (y)}{\ln (2)}, y > 0}