2=(1.01)^n

how do you solve for n

log 2 = n log 1.01

n = log 2 / log 1.01

To solve for n in the equation 2 = (1.01)^n, we can use logarithms. Specifically, the natural logarithm (ln) can be used. Here's how you can solve it step by step:

1. Take the natural logarithm (ln) of both sides of the equation:
ln(2) = ln((1.01)^n)

2. Apply the property of logarithms: ln(a^b) = b * ln(a)
ln(2) = n * ln(1.01)

3. Divide both sides of the equation by ln(1.01) to isolate n:
n = ln(2) / ln(1.01)

4. Use a calculator to evaluate the division:
n ≈ 69.6607

Therefore, the value of n in the equation 2 = (1.01)^n is approximately 69.6607.