Find the value of x to 2 decimal places: 3 × 3 x = 15 .

Given that, we have: 3 × 3 x = 15 ⇒ 3 x = 5 An exponential equation has the form a x = b a is the base x is the exponent or power For any two positive numbers a and b , there exists a third number c , so that you can write the exponential statement a c = b or the equivalent logarithmic statement log a b = c ; a , b > 0 and a ≠ 1 So, rewriting as the logarithmic statement log 3 5 = x ⇒ x = log 10 5 log 10 3 [Use change of base formula] ⇒ x = 0 . 6989 0 . 4771 [Use logarithmic calculator] ⇒ x = 1 . 46489206 ∴ x = 1 . 46 [To two decimal places]

Find the value of x to 2 decimal places: 2 × 3 2 x + 1 = 45 .

Given that, we have: 2 × 3 2 x + 1 = 45 ⇒ 2 × 3 2 x × 3 = 45 ⇒ 2 × 3 2 x = 15 ⇒ 3 2 x = 15 2 ⇒ 9 x = 15 2 An exponential equation has the form a x = b a is the base x is the exponent or power For any two positive numbers a and b , there exists a third number c , so that you can write the exponential statement a c = b or the equivalent logarithmic statement log a b = c ; a , b > 0 and a ≠ 1 So, rewriting as the logarithmic statement log 9 15 2 = x ⇒ x = log 10 15 2 log 10 9 [Use change of base formula] ⇒ x = log 10 15 2 log 10 3 2 ⇒ x = - log 10 2 15 2 log 10 3 ⇒ x = 0 . 91702188 . . . [Use logarithmic calculator] ∴ x = 0 . 92 [To two decimal places]