Questions: Solve the exponential equation using the method of "relating the bases" by first rewriting the equation in the form b^u=b^V 11^x=121

Transcript text: Solve the exponential equation using the method of "relating the bases" by first rewriting the equation in the form $\mathrm{b}^{\mathrm{u}}=\mathrm{b}^{\mathrm{V}}$ \[ 11^{x}=121 \]

Solution

Solution Steps

To solve the exponential equation $11^x = 121$ using the method of "relating the bases," we first express 121 as a power of 11. Since $121 = 11^2$, we can rewrite the equation as $11^x = 11^2$. By relating the bases, we equate the exponents, giving us $x = 2$.

Step 1: Rewrite the Equation

We start with the equation: \[ 11^x = 121 \] Next, we express $121$ as a power of $11$: \[ 121 = 11^2 \] Thus, we can rewrite the equation as: \[ 11^x = 11^2 \]

Step 2: Relate the Exponents

Since the bases are the same, we can equate the exponents: \[ x = 2 \]