Change the exponentional expression to an equivalent expression involving a logarithm.

(2x)^-10=4

-10 log 2x = log 4

I always encouraged my students to memorize this statement

23 = 8 <------> log2</sub) 8 = 3

that way you will be able to convert easily in either direction

log (2x)4 = -10

23 = 8 <-----> log 2 8 = 3

log2x 4 = -10

To change the exponential expression (2x)^-10=4 into an equivalent expression involving a logarithm, we can use the logarithmic property that states:

If b^x = y, then log base b of y = x.

Using this property, we can rewrite the given expression as:

log base (2x) of 4 = -10

Therefore, the equivalent expression involving a logarithm is log base (2x) of 4 = -10.