Change the logarithmic equation to an equivalent equation involving an exponent.
log8^64=2
**note that the 8 should be lower than the g**
8^(log64)=8^2
64=8^2
is this correct
You are correct
you could just use the definition.
I used to tell my students to "memorize" the following pattern
2^3 = 8 <-------> log2 8 = 3
that way you can tell what goes where.
Yes, your approach is correct. To change a logarithmic equation to an equivalent equation involving an exponent, you need to understand the properties of logarithms.
In this case, the given equation is: log8^64 = 2
To change it to an equivalent equation involving an exponent, you want to convert the logarithm to exponent form using the definition of logarithms.
The definition of logarithms states that log base b of x is equal to y if and only if b^y = x.
Applying this definition to your equation, you can rewrite it as: 8^2 = 64
Simplifying further, you get: 64 = 64
Since this equation is true, your conversion is correct, and the original logarithmic equation log8^64 = 2 is equivalent to the exponent equation 8^2 = 64.