Question

Which logarithmic equation is equivalent to 8^2 =64

Answer 1

㏑(8^2) = ㏑(64)
or
㏑(a^n) = n㏑(a)
so
2㏑(8) = ㏑(64)

Is it what you mean by logarithmic equation ?

Answer 2

`\log_8(64) = 2`

Explanation:

We are given an equation:

`8^2 = 64`

We have to convert this into a logarithmic equation.

We know that:

`b^x = a`

where b is the base and x is the exponent.

Then, it can be written as:

`\log_b(a) = x`

So, we have b = 8, x = 2 and a = 64

Thus, we can write:

`\bold{\log_8(64) = 2}`

It is the required logarithmic equation.