Question

How do you solve `(1/7)^(y-3)=343`?

Answer 1

Please see the explanation for steps leading to the answer: `y =0`

Explanation:

Given:

`(1/7)^(y - 3) = 343`

Take the natural logarithm on both sides:

`ln((1/7)^(y - 3)) = ln(343)`

Use the property of logarithms `log_b(a^c) = (c)log_b(a)` on the left side:

`(y - 3)ln(1/7) = ln(343)`

Divide both sides by `ln(1/7)`:

`y - 3 = ln(343)/ln(1/7)`

Use the property of logarithms `log_b(1/a) = -log_b(a)` on the `ln(1/7)`:

`y - 3 = ln(343)/-ln(7)`

Add 3 to both sides:

`y = 3 - ln(343)/ln(7)`

`y = 0`

Answer 2

`y=0`

Explanation:

`(1/7)^(y-3)=343`

now `7^3=343`

& `(1/7)^-1=7`

`:.(1/7)^(y-3)=7^(3-y)`

`7^(y-3)=7^3=343`

`=>y-3=0`

`:.y=0`