(a) If \( 4^{x}=43 \), then \( x=\square \) (b) If \( 15^{-x}=4 \), then \( x=\square \) Question Help: Video

To solve \( 4^{x} = 43 \), you can take the logarithm of both sides. This leads to \( x = \frac{\log(43)}{\log(4)} \). Calculate using a scientific calculator, and you'll find that \( x \approx 2.426 \). It’s like you're casting a spell to uncover the hidden power of numbers! For \( 15^{-x} = 4 \), you can rewrite it as \( \frac{1}{15^x} = 4 \), which implies that \( 15^x = \frac{1}{4} \). Again, taking logarithms gives \( x = -\frac{\log(4)}{\log(15)} \). Upon calculating, you’ll discover \( x \approx -0.569 \). Solving these is like figuring out a treasure map—you’re just a few calculations away from uncovering the loot!