Questions: Solve, Simplify your answer: 7 log t=7 t=

Transcript text: Solve, Simplify your answer: \[ \begin{array}{l} 7 \mathrm{log} t=7 \\ t=\square \end{array} \]

Solution

Solution Steps

To solve the equation \(7 \log t = 7\), we first divide both sides by 7 to isolate the logarithm. This gives us \(\log t = 1\). Next, we convert the logarithmic equation to its exponential form, which is \(t = 10^1\).

Step 1: Isolate the Logarithm

Given the equation \(7 \log t = 7\), we start by dividing both sides by 7 to isolate the logarithm: \[ \log t = 1 \]

Step 2: Convert to Exponential Form

Next, we convert the logarithmic equation to its exponential form. Since \(\log t = 1\) implies that the base 10 logarithm of \(t\) is 1, we have: \[ t = 10^1 \]

Step 3: Simplify the Exponential Expression

Simplifying the expression \(10^1\) gives: \[ t = 10 \]