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*10^(29)`

Now, we take natural logarithm to both sides:

`\ln 2^n=\ln 3.2*10^(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*10^(29)`

Now, we divide both sides by ln 2:

`n=(\ln 3.2*10^(29))/(\ln 2)`

Solving the operations we get:

`n=98`

Therefore, the value of "n" is 98.