Question

How do you solve ${{8}^{x}}=64$?

Answer 1

Hint: The given question is quite easy; you need to convert the number 64 to the base of 8 after that with the help of exponent laws we can easily simplify the equation ${{8}^{x}}=64$. You need to make the bases the same. So, let’s see how we can solve this.

Complete Step by Step Solution:
The given equation is ${{8}^{x}}=64$.
Now, the first thing which we need to do is to make the number 64 to the base of 8, which means ${{8}^{2}}=64$.
So, when we put the value of 64 in the above equation, we get,
$\Rightarrow {{8}^{x}}={{8}^{2}}$
As, both the bases are the same we can clearly state by the law of exponent that the value of x=2.

Therefore, after simplifying the given equation we get the value of x=2.

Additional Information:
In the above question, we used exponent law. There are several other exponent laws such as Multiplication rule, Division rule, Zero exponents, Negative exponent, Fractional exponent, power of a power rule, Power of a product rule, and Power of a fraction rule. These small laws are quite helpful in solving the problem.

Note:
There is an alternative way for the above equation.
We can deduce the equation with the help of a logarithmic table or calculator by converting it to the logarithmic form, that means when we apply log to both the sides of the given equation ${{8}^{x}}=64$, we get,
$\Rightarrow x\log 8=\log 64$
Now taking the log 8 to the right-hand side, we get,
$\Rightarrow x=\dfrac{\log 64}{\log 8}$
Now, with the help of a logarithmic table or calculator put the value of 64 and 8 as, 1.81 and 0.9 and solving them, we get,
$\Rightarrow x=\dfrac{1.81}{0.9}=2$
Therefore, after simplifying the given equation we get the value of x=2.