Question
Question: How do you solve \( {2^x} = 15 \) ?...
How do you solve 2x=15 ?
Solution
Hint : To find the answer to the above question, our first approach should be to separate the unknown variable on one side of the equation. To do so we will take logs on both sides of the equation. This step will bring us a point where the unknown variable will be equal to a value of logylogx . Here, we will use the logarithm property that logylogx=logyx to simplify the answer to the best possible version. Also, calculators can be used in the final step to get the values of log in order to get the most precise answer.
Complete step-by-step answer :
The given equation in the question is
2x=15
Now, in order to simplify this equation more to find the answer we have to separate the x and keep it on one side of the equation and the rest on the other
So, to do that we will take log on both the sides
Therefore,
log2x=log15
Now using the property of log which says logxy=ylogx
log2x becomes, xlog2
Hence,
xlog2=log15 ⇒x=log2log15
Now, another property of logarithm states that logylogx=logyx
Hence,
x=log2log15 =log215
Therefore the solution of 2x=15 is x=log215 .
So, the correct answer is “ x=log215 ”.
Note : One can directly put values of log 15 and log 2 to calculate the value of x in the steps above. But in cases when you don’t know the value of the logarithmic numbers then just try to simplify the numbers as much as possible. The most simplified version of the numbers would suffice for the final answer of the question