To solve the equation $49^x = 343$, what is the most efficient common base to use for rewriting both sides of the equation?

It is not possible to use a common base.

Solving Exponential Equations Practice — Grade 8 math

1. Solve the exponential equation for the variable $x$: $4^{x+2} = 8^x$. The value of $x$ is ___.
2. To solve the equation $49^x = 343$, what is the most efficient common base to use for rewriting both sides of the equation?
- A. 3
- B. 7
- C. 49
- D. It is not possible to use a common base.
3. Find the value of $x$ that satisfies the equation $25^x = \frac{1}{5^{x-9}}$. The value of $x$ is ___.
4. If $16^{x-1} = 64^x$ is rewritten using a common base of 2, which equation correctly represents the relationship between the exponents?
- A. $4(x-1) = 6x$
- B. $2(x-1) = 3x$
- C. $x-1 = x$
- D. $16x - 16 = 64x$
5. Solve for $x$ in the equation $27^{x+1} = 9^{2x}$. The value of $x$ is ___.
6. How many real solutions does the equation $5^x = -25$ have?
- A. 0
- B. 1
- C. 2
- D. Infinitely many
7. Solve for $x$ in the equation $3^x = 81$. The value of $x$ is ___.
8. The equation $9^x - 10 \cdot 3^x + 9 = 0$ has two solutions. What is the sum of these solutions? The sum is ___.
9. Which of the following exponential equations can have more than one real solution?
- A. $4^x = 16$
- B. $3^x = -9$
- C. $(2^x)^2 - 6(2^x) + 8 = 0$
- D. $5^x = 1$
10. How many real solutions does the equation $2 \cdot 10^x + 8 = 4$ have? The number of solutions is ___.