Questions: The logarithmic equation log10 x=9 written as an exponential equation is □

Solution Steps

To convert a logarithmic equation to an exponential equation, we use the property that if \(\log_b a = c\), then \(b^c = a\). In this case, \(\log_{10} x = 9\) can be rewritten as \(10^9 = x\).

We start with the given logarithmic equation: \[ \log_{10} x = 9 \]

Using the property of logarithms, \(\log_b a = c\) implies \(b^c = a\). Here, \(b = 10\), \(c = 9\), and \(a = x\). Therefore, we can rewrite the equation as: \[ 10^9 = x \]

Calculate \(10^9\): \[ 10^9 = 1,000,000,000 \]

Final Answer