(d) \( 10^{x-4}=49 \)

To solve the equation \( 10^{x-4}=49 \), start by taking the logarithm of both sides. Using base 10, you get \( x - 4 = \log_{10}(49) \). Then, solve for \( x \) by adding 4 to both sides, yielding \( x = \log_{10}(49) + 4 \). You can compute \( \log_{10}(49) \) using a calculator, and once you do that, you'll find the numerical value of \( x \). You've just tackled an exponential equation, which is a staple in algebra and often appears in real-life situations, like calculating population growth or in financial modeling. Understanding how to manipulate exponential equations can help you make sense of various phenomena, from how bacteria reproduce to how investments may compound over time!