Solve for x in the logarithmic equation 10log(10^24)=10x .(1 point)

Answer 1

To solve the equation \( 10 \log(10^{24}) = 10x \), we start by simplifying the left side.

Recall that the logarithm of a power can be simplified using the property:

\[ \log(a^b) = b \log(a) \]

Applying this to our equation:

\[ \log(10^{24}) = 24 \log(10) \]

Since \(\log(10) = 1\), we have:

\[ \log(10^{24}) = 24 \cdot 1 = 24 \]

Now substituting back into the original equation:

\[ 10 \cdot 24 = 10x \]

This simplifies to:

\[ 240 = 10x \]

Next, we solve for \(x\) by dividing both sides by 10:

\[ x = \frac{240}{10} = 24 \]

Therefore, the solution is:

\[ \boxed{24} \]

Answer 2

If 10logx=10^18 , what is the value of x?(1 point)

Answer 3

To solve the equation \( 10 \log x = 10^{18} \), we start by dividing both sides by 10:

\[ \log x = 10^{17} \]

Next, we can rewrite the logarithmic equation in exponential form:

\[ x = 10^{10^{17}} \]

Thus, the value of \( x \) is:

\[ \boxed{10^{10^{17}}} \]