Convert each expression to an expression with the indicated

Convert each expression to an expression with the indicated base. a)

a) 7^(x-1) to base e

b) log3(x+2) to base 10

Solution

a) 7^(x-1) to base e

let y =  7^(x-1)

apply ln on both sides

lny = ln 7^(x-1)

lny = (x-1) ln7

y = e^(x-1) ln7

b). log3(x+2) to base 10

let y = log3(x+2)

logy = log log3(x+2)

y = 10^( log log3(x+2))