Question

how to calculate log without using calculater?
7 = 3^x

Answer 1

To calculate logarithms without a calculator, we can use logarithmic properties and solve for x.

In this case, we have the equation: 7 = 3^x

To solve for x, we can take the logarithm of both sides of the equation using any base. Common logarithm (base 10) or natural logarithm (base e) are usually used for ease of calculation. Let's use the natural logarithm (ln) in this example.

ln(7) = ln(3^x)

Using the logarithmic property ln(a^b) = b * ln(a), we can simplify the equation further:

ln(7) = x * ln(3)

Now, let's isolate x:

x = ln(7) / ln(3)

Using a scientific calculator or an online calculator if needed, we can calculate the natural logarithm of 7 divided by the natural logarithm of 3 to find the value of x.