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

Transcript text: \[ \log _{10} x=9 \] The logarithmic equation $\log _{10} x=9$ written as an exponential equation is $\square$

Solution

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 $10^9 = x$.

Step 1: Identify the Logarithmic Equation

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

Step 2: Convert to Exponential Form

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: \[ 10^9 = x \]

Step 3: Calculate the Exponential Value

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