log9 1= _______ (fill in the blank)

Let x=log2 1/32 . Write the exponential form of the equation and solve the equation for x.

a)

Log 1 to any base is zero.

x = log21/32
= -log2 32
= -log225
= -5

Note:
lognnx
= x

LOG5(X+7)=LOG3(X-4)+LOG3(X_2-LOG3 X=

To find the answer to the first question, "log9 1 = _______", we need to understand the concept of logarithms.

In general, the logarithm of a number is the exponent to which another fixed number, called the base, must be raised to produce that number. In this case, we are looking for the logarithm of 1 to the base 9.

To solve this, we need to determine what exponent we need to raise 9 to, in order to get 1. In other words, we need to find x such that 9^x = 1.

The answer here is x = 0, because any number raised to the power of 0 equals 1. Therefore, log9 1 is equal to 0.

Now, moving on to the second question, we are given x = log2 (1/32) and we need to write the exponential form of the equation and solve it for x.

To do this, we can rewrite the equation in exponential form. Recall that if y = logb(x), then b^y = x.

Applying this principle, we have 2^x = 1/32.

To solve for x, we can observe that 1/32 can be rewritten as 2^(-5).

Therefore, we can equate the exponents: 2^x = 2^(-5).

Since the bases are the same, we can set the exponents equal to each other: x = -5.

Therefore, the solution to the equation x = log2 (1/32) is x = -5.