<prompt> Theha tšebetso ea logarithmic ka lintlha tse fanoeng tsa dataXY 2 4 4 16 8 256  <response>: Instruction in English: Construct a logarithmic function with the given data points . Response in English: The given data points suggest that this is an exponential function where Y increases rapidly as X increases. We can use logarithms to determine the equation of the function that passes through these points. Since the function is exponential, we are going to use the general form of the function as such:y abx.First, well use the first data point 2,4 to find the value of b:4 ab2Next, well use the second data point 4,16 to find the value of a:16 ab4Dividing the second equation by the first equation well get:4 b4-24 b2b 2And substituting the value of b to the first equation above, well get:4 a 224 4aa 1Therefore, the logarithmic function that passes through the given data points is:y 2x. . Response in Sesotho: Lintlha tse fanoeng tsa data li fana ka maikutlo a hore sena ke tsebetso ea exponential moo Y e eketsehang ka potlako ha X e eketseha. Re ka sebelisa li-logarithms ho fumana hore na equation ea tsebetso e fetang lintlheng tsena ke efe. Kaha tsebetso ke exponential, re tla sebelisa mokhoa o akaretsang oa tsebetso joalo ka: y abx. Taba ea pele, re tla sebelisa ntlha ea data ea pele 2,4 ho fumana boleng ba b: 4 ab2 Ka mora moo, re tla sebelisa ntlha ea bobeli ea data 4,16 ho fumana boleng ba a: 16 ab4 Ho arola palo ea bobeli ka equation ea pele re tla fumana: 4 b4-2 4 b2 b 2 Le ho beha boleng ba b ho equation ea pele. ka holimo, re tla fumana: 4 a 22 4 4a a 1 Ka hona, mosebetsi oa logarithmic o fetang ka lintlha tse fanoeng ke data ke: y 2x. 