Question

Log(7) 1/7 = ?

7ˣ= 1/7
x = ?

Answer 1

The answer to log(7) 1/7 is -1, as logarithm of a reciprocal is the negative of the logarithm of the number. Similarly, for the equation 7^x = 1/7, x equals -1 because 1/7 is 7 raised to the power of -1.

Step-by-step explanation:

To solve the equation log(7) 1/7, we'll use the property of logarithms where the logarithm of the reciprocal is the negative of the logarithm of the number itself.

Therefore, since 7 is the base and 1/7 is the reciprocal of 7, log(7) 1/7 is -1.

For the second equation, 7^x = 1/7, we want to find the value of x. Recognizing that 1/7 is 7 to the power of -1, we can see that x must be -1 as well, since 7 raised to the power negative 1 equals 1/7.

The principle of the logarithm's property used in the first question is analogous to the principle that the logarithm of a number resulting from the division of two numbers is the difference between the logarithms of the two numbers.

Answer 2

Heres a trick I like to do in the calculator when I can’t figure it out
(log(10)1/7)/(log(10)7)

So basically use the basic log on your calculator which is log10 (log with the base of 10) and put the number you are solving for on top and the original base of the log on the bottom.

Another thing is we know that x will be negative since 7^x is a fraction.

So the answer is x=-1