Answer :
The equation 2^x = 128 as a logarithmic equation is log₂(128) = x
How to rewrite the equation as a logarithmic equation?
The equation is given as:
2^x = 128
Take the logarithm of both sides
log(2^x) = log(128)
Rewrite as:
x * log(2) = log(128)
Divide both sides of the equation by log(2)
x = log(128)/log(2)
Apply the change of base rule
x = log₂(128)
Hence, the equation 2^x = 128 as a logarithmic equation is log₂(128) = x
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The equation 2ˣ = 128, when rewritten as a logarithmic equation, becomes log₂(128) = X. The logarithm asks for the power to which the base (in this case, 2) must be raised to achieve the number 128.
To convert the equation 2ˣ = 128 to a logarithmic form, we need to understand what a logarithm represents. A logarithm with a base b of a given number x is the power to which b must be raised to produce x.
When 2 is raised to the power of x to equal 128, we are looking for the exponent x such that 2x = 128, which is indeed a logarithmic relationship. In this case, the base b is 2 and the number x is 128.
Therefore, the logarithmic form of the equation is log₂128 = x.