Question

Convert the logarithmic expression log(base b) x = y to its equivalent exponential form.

a) x = b^y
b) y = b^x
c) b = x^y
d) x = y^b

Answer 1

The logarithmic expression log(base b) x = y converts to the exponential form x = b^y, where base b raised to the power y equals x.

Step-by-step explanation:

To convert the logarithmic expression log(base b) x = y to its equivalent exponential form, we need to understand the relationship between logarithms and exponents. Logarithms are the inverse operations of exponents. The definition of a logarithm states that if log(base b) x = y, then b raised to the power of y is x.

This means that the base b, when raised to the exponent y, gives the number x. Therefore, the equivalent exponential form of the logarithmic expression is x = b^y.

To convert the logarithmic expression log(base b) x = y to its equivalent exponential form, we need to understand the relationship between logarithms and exponentials. In exponential form, the base (b) is raised to the exponent (y) and equals the result (x). Therefore, the correct answer is a) x = b^y.

For further clarity, if we were given log28 = 3 in logarithmic form, converting this to exponential form would give us 23 = 8, which confirms our understanding as 2 raised to the power of 3 indeed equals 8.

Therefore answer is a) x = b^y.