If y=7^(x+5)write the equation for the inverse of y. It must be a y=equation.
Y = 7^(x+5),
X= 7^(y+5),
Take log of both sides:
(y+5)log7 = logX,
Divide both sides by log of 7:
y+5 = logX / log7,
y+5 = logX / 0.8451,
y+5 = 1.183*logX,
y+5 = X^(1.183),
Y = X^(1.18 - 5.
CORRECTION.
Y = X^(1.18) - 5.
To find the inverse of a function, we need to interchange the roles of x and y and solve for the new y.
Given y = 7^(x+5), let's swap x and y variables:
x = 7^(y+5)
Now, let's solve for y by taking the logarithm of both sides (base 7 since the exponent is 7):
log base 7 of x = y + 5
To rewrite this equation in the form y = f(x), we can subtract 5 from both sides:
y = log base 7 of x - 5
Therefore, the equation for the inverse of y is y = log base 7 of x - 5.