0.99+left(1-0.25right)^N=1-এর সমাধান করুন

$$0.99+{\left(1-0.25\right)}^{N}=1$$

Solve for N

$$N=-2\log_{0.75}\left(10\right)\approx 16.007845559$$

Steps Using Definition of Logarithm

Subtract 0.25 from 1 to get 0.75.

$$0.99+0.75^{N}=1$$

Subtract 1 from both sides.

$$0.99+0.75^{N}-1=0$$

Subtract 1 from 0.99 to get -0.01.

$$-0.01+0.75^{N}=0$$

Use the rules of exponents and logarithms to solve the equation.

$$0.75^{N}-0.01=0$$

Add 0.01 to both sides of the equation.

$$0.75^{N}=0.01$$

Take the logarithm of both sides of the equation.

$$\log(0.75^{N})=\log(0.01)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$N\log(0.75)=\log(0.01)$$

Divide both sides by \log(0.75).

$$N=\frac{\log(0.01)}{\log(0.75)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$N=\log_{0.75}\left(0.01\right)$$