Which is equivalent to y=log of 7(x)

a)y=x^7
b)x=y^7
c) x=7^y
d) y=x^1/7
I thought the answer was c x=7^y
Is this correct? thank you

yes

thank you!

No, the correct answer is d) y=x^(1/7).

To determine the equivalent expression for y=log base 7 of x, we need to rewrite the logarithmic equation in exponential form. In logarithmic form, it is written as y=log7(x), which means that 7 raised to the power of y equals x.

In exponential form, the equivalent expression is x=7^y. However, the given options do not match this form. The correct equivalent expression is y=x^(1/7), which is option d).

To determine the equivalent expression to y = log of 7(x), we need to understand the properties of logarithms.

The given equation y = log of 7(x) represents a logarithmic equation with base 7. Recall that the logarithm function in base 7 calculates the exponent to which 7 must be raised to obtain a particular value, indicated inside the parentheses.

Since we want to find an equivalent expression, we need to rewrite the equation in exponential form.

In exponential form, log base 7 of x = y can be written as 7^y = x.

Examining the options provided:
a) y = x^7 - This expression raises x to the power of 7, not 7 to the power of y, so it is not equivalent to the original equation.
b) x = y^7 - This expression raises y to the power of 7, not 7 to the power of y, so it is not equivalent to the original equation.
c) x = 7^y - This expression matches the exponential form of the original equation, so it is equivalent and could be the correct answer.
d) y = x^(1/7) - This expression raises x to the power of 1/7, not 7 to the power of y, so it is not equivalent to the original equation.

Based on the analysis above, the correct answer is c) x = 7^y.