(a) If \( \log _{x} 9=2 \), then \( x=\square \) (b) If \( \log _{x} 256=4 \), then \( x=\square \) Question Help: \( \square \) Video

To solve \( \log_{x} 9 = 2 \), we know that this means \( x^{2} = 9 \). Taking the square root gives us \( x = 3 \) (considering positive bases). For \( \log_{x} 256 = 4 \), this implies \( x^{4} = 256 \). Since \( 256 = 4^4 \), we can deduce that \( x = 4 \). Logs might seem tricky, but they’re just a fun way to express relationships between numbers! For example, if you ever find yourself stuck, remember that the antilogarithm is simply the opposite of taking a log. Just like if you notice a mistake in your log calculations, it’s often wise to recheck your base values and ensure no sneaky arithmetic errors slipped by!