Question
Question: How do you solve \( {10^x} = 75 \) ?...
How do you solve 10x=75 ?
Solution
Hint : Use logarithm to solve this problem because we cannot solve this problem in a conventional method. So, use logarithm to solve this problem. It is one of the complicated problems to deal with. Here 10x is the hint, which indirectly tells us to use logarithm.
Complete step-by-step answer :
Let’s consider the given problem,
10x=75
Taking log on both sides we get,
log10x=log75
And we know that in logarithm, the power value can be brought as the multiples of the base number i.e.., log2x can be written as xlog2 , applying this to the given equation we get,
xlog10=log75
Substituting the value log10=1 in above equation we get,
x=log75
Substituting the value for log75=1.8750 in above equation,
x=1.8750
This is our required solution.
So, the correct answer is “ x=1.8750 ”.
Note : As I mentioned already it is one of the complicated problems in mathematics, there are also some uncomplicated problems in this concept. For instance, let us consider a problem 5x=625 , here we need to convert 625 in terms of 5 to the power of some number. Here if we put 54 , we will get the value 625 . Hence the problem becomes, 5x=54 , if the bases are the same, we can equate the powers and hence x is equal to 4 .