To solve this equation, we can start by adding 1 to both sides of the equation:
9^z - 1 + 1 = 2 + 1
9^z = 3
Next, we can take the logarithm of both sides of the equation to solve for z. Let's use the natural logarithm (ln):
ln(9^z) = ln(3)
By applying the logarithmic property for exponentiation (z ln a = ln(a^z)), we can rewrite the left side of the equation:
z ln 9 = ln 3
Finally, we divide both sides of the equation by ln 9 to solve for z:
z = ln 3 / ln 9
Using a calculator, we can find that ln 3 ≈ 1.0986 and ln 9 ≈ 2.1972. Therefore,
z ≈ 1.0986 / 2.1972 ≈ 0.5
So the solution to the equation is z ≈ 0.5.
Therefore, the answer is A. 1/2.
What is the solution to this equation?
9^z-1=2
A. 1/2
B. 1
C. 2
D. -1/2
1 answer