Exercise 73 Page 483

To solve the given exponential equation, we will start by applying inverse operations and the Properties of Equality to isolate the term with the exponent. 7^x -2 = 252 ⇔ 7^x = 254When bases are not the same, we can solve the equation by taking the logarithm of each side of the equation. m=n ⇔ log m = log n Note that in order to take their logarithms, both m and n must be positive numbers. Let's now solve our equation.

7^x=254

log_()(LHS)=log_()(RHS)

log 7^x = log 254

log_()(a^m)= m* log_()(a)

x log 7 = log 254

DivEqn

.LHS /log 7.=.RHS /log 7.

x=log 254/log 7

UseCalc

Use a calculator

x ≈ 2.846