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Question

Question: How do you solve \( {10^x} = 75 \) ?...

How do you solve 10x=75{10^x} = 75 ?

Explanation

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{10^x} is the hint, which indirectly tells us to use logarithm.

Complete step-by-step answer :
Let’s consider the given problem,
10x=75{10^x} = 75
Taking log\log on both sides we get,
log10x=log75\log {10^x} = \log 75
And we know that in logarithm, the power value can be brought as the multiples of the base number i.e.., log2x\log {2^x} can be written as xlog2x\log 2 , applying this to the given equation we get,
xlog10=log75x\log 10 = \log 75
Substituting the value log10=1\log 10 = 1 in above equation we get,
x=log75x = \log 75
Substituting the value for log75=1.8750\log 75 = 1.8750 in above equation,
x=1.8750x = 1.8750
This is our required solution.
So, the correct answer is “ x=1.8750x = 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{5^x} = 625 , here we need to convert 625625 in terms of 55 to the power of some number. Here if we put 54{5^4} , we will get the value 625625 . Hence the problem becomes, 5x=54{5^x} = {5^4} , if the bases are the same, we can equate the powers and hence xx is equal to 44 .