How do you linearize the exponential equation y = ab^x?

Question

ScanSolve AI Tutor · Accepted Answer

To linearize the equation y = ab^x, we take the natural logarithm of both sides. Step 1: Start with the given equation. y = ab^x Step 2: Take the natural logarithm (ln) of both sides. ln(y) = ln(ab^x); Step 3: Use the logarithm property ln(MN) = ln(M) + ln(N) to separate the terms on the right side. ln(y) = ln(a) + ln(b^x); Step 4: Use the logarithm property ln(M^P) = P ln(M) to bring the exponent x down. ln(y) = ln(a) + x ln(b); Step 5: Rearrange the equation into the standard linear form Y = mX + c. ln(y) = (ln(b))x + ln(a); Here, Y = ln(y), X = x, the slope m = ln(b), and the y-intercept c = ln(a). The linearized equation is: ln(y) = (ln(b))x + ln(a)

How do you linearize the exponential equation y = ab^x?

Answer

Step-by-step solution

Start with the given equation.

Take the natural logarithm ( $\ln$ ) of both sides.

Use the logarithm property $\ln(MN) = \ln(M) + \ln(N)$ to separate the terms on the right side.

Use the logarithm property $\ln(M^P) = P \ln(M)$ to bring the exponent $x$ down.

Rearrange the equation into the standard linear form $Y = mX + c$ .

Try one yourself

Still stuck on this one?

More Mathematics Questions

How do you linearize the exponential equation y = ab^x?

Answer

Step-by-step solution

Start with the given equation.

Take the natural logarithm (ln⁡\lnln) of both sides.

Use the logarithm property ln⁡(MN)=ln⁡(M)+ln⁡(N)\ln(MN) = \ln(M) + \ln(N)ln(MN)=ln(M)+ln(N) to separate the terms on the right side.

Use the logarithm property ln⁡(MP)=Pln⁡(M)\ln(M^P) = P \ln(M)ln(MP)=Pln(M) to bring the exponent xxx down.

Rearrange the equation into the standard linear form Y=mX+cY = mX + cY=mX+c.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Take the natural logarithm ( $\ln$ ) of both sides.

Use the logarithm property $\ln(MN) = \ln(M) + \ln(N)$ to separate the terms on the right side.

Use the logarithm property $\ln(M^P) = P \ln(M)$ to bring the exponent $x$ down.

Rearrange the equation into the standard linear form $Y = mX + c$ .