change the logarithmic expression to an equivalent expression involving an exponent. 4^16=x
log (base4)16=x
is it x=e^2?
To change the logarithmic expression log (base 4) 16 to an equivalent expression involving an exponent, you can use the definition of logarithms.
In general, logarithms relate exponents to a given base. In this case, the logarithm log (base 4) 16 means "the exponent to which 4 must be raised to obtain 16".
To rewrite this logarithmic expression in terms of an exponent, you need to express the base 4 as the base of an exponent.
So, the equivalent exponential expression would be 4^x = 16.
Now, to determine the value of x, you can solve the equation 4^x = 16.
Taking the logarithm (base 4) of both sides, you get:
log (base 4)(4^x) = log (base 4)(16).
Using the logarithmic property that log (base a)(a^x) = x, the equation simplifies to:
x = log (base 4)(16).
At this point, you can evaluate the logarithm using the given base 4. Since 4^2 = 16, it follows that log (base 4)(16) = 2.
Therefore, x = 2.
So the correct value of x is x = 2, not x = e^2.