How do I rewrite log4 1=0 as an equivalent exponential equation? How do I rewrite 4 to the -2 power = 1/16 as an equivalent logarithmic equation? Any help is greatly appreciated.
If 4 is the BASE of the logarithm, then
log (1) = 0 means
...4
4^0 = 1
4^(-2) = 1/16 can be written
log (1/16) = -2
...4
I wrote the number 4, the base of the logarithms in the case, on a lower line, since I don't know how to type subscripts here.
To rewrite log4 1=0 as an equivalent exponential equation, you can use the definition of logarithm. In this case, the base of the logarithm is 4, the value inside the logarithm is 1, and the result is 0.
So, to rewrite it as an exponential equation, you can raise the base (4) to the power of the result (0). This gives you:
4^0 = 1
Therefore, the equivalent exponential equation is 4^0 = 1.
Now, to rewrite 4 to the -2 power = 1/16 as an equivalent logarithmic equation, you need to use the definition of exponentiation.
The equation states that 4 raised to the power of -2 is equal to 1/16.
To write this as a logarithmic equation, you can express it in terms of the logarithm base 4.
So, the logarithmic equation is log4 (1/16) = -2.
Keep in mind that the base of the logarithm is written to the right of the "log". In this case, since it's not possible to type subscripts here, the base 4 is displayed below the "log".