Question

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

Answer 1

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

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