2=(1.01)^n
how do you solve for n
Take logarithms of both sides, to any base. I will use base 10 below
log 2 = n log 1.01
n = 0.301030/0.00432137 = 69.66
To solve for n in the equation 2 = (1.01)^n, you can follow these steps:
Step 1: Take the natural logarithm (ln) of both sides of the equation to remove the exponent:
ln(2) = ln[(1.01)^n]
Step 2: Apply the logarithmic property that states ln(a^b) = b * ln(a):
ln(2) = n * ln(1.01)
Step 3: Divide both sides of the equation by ln(1.01) to isolate n:
n = ln(2) / ln(1.01)
Step 4: Use a calculator to evaluate the right side of the equation to find the approximate value of n. The result is approximately:
n ≈ 69.66
Therefore, n is approximately 69.66.
To solve for n in the equation 2 = (1.01)^n, you can use logarithms. Here's a step-by-step explanation of how to solve it:
Step 1: Take the logarithm of both sides of the equation. The choice of logarithm base is up to you, but the common logarithm (log with base 10) or the natural logarithm (ln with base e) are commonly used. Let's use the natural logarithm in this case.
ln(2) = ln((1.01)^n)
Step 2: Apply the property of logarithms that states log(xy) = y * log(x) to simplify the equation. In this case, we have n * ln(1.01):
ln(2) = n * ln(1.01)
Step 3: Divide both sides of the equation by ln(1.01) to solve for n:
n = ln(2) / ln(1.01)
Using a calculator or an online logarithm calculator, compute ln(2) and ln(1.01), then divide ln(2) by ln(1.01) to find the value of n.
Note: The solution should be a real number, which represents the exponent n required to raise 1.01 to in order to obtain 2.