Question

2^n+2^98=2^99 what does n =

Answer 1

We are given the following equation:

$2^n+2^{98}=2^{99}$

We are asked to solve for "n". To do that we will first subtract 2 to the 98 from both sides:

$2^n=2^{99}-2^{98}$

Solving the operations we get:

$2^n=3.2\times10^{29}$

Now, we take natural logarithm to both sides:

$\ln 2^n=\ln 3.2\times10^{29}$

Now, we use the following property of logarithms:

$\ln x^y=y\ln x$

Applying the property we get:

$n\ln 2=\ln 3.2\times10^{29}$

Now, we divide both sides by ln 2:

$n=\frac{\ln 3.2\times10^{29}}{\ln 2}$

Solving the operations we get:

$n=98$

Therefore, the value of "n" is 98.