Take the natural logarithm (ln) of both sides of the equation.

Here are the solutions for the parameter x in each case: a) For science Vs library blocks: 3^2x-1 = 5^x Step 1: Take the natural logarithm (ln) of both sides of the equation. (3^2x-1) = (5^x) Step 2: Apply the logarithm property (a^b) = b a to both sides. (2x-1) 3 = x 5 Step 3: Distribute 3 on the left side. 2x 3 - 3 = x 5 Step 4: Gather terms containing x on one side and constant terms on the other. 2x 3 - x 5 = 3 Step 5: Factor out x from the terms on the left side. x(2 3 - 5) = 3 Step 6: Solve for x. x = ( 3)/(2 3 - 5) Using logarithm properties, 2 3 = (3^2) = 9. x = ( 3)/( 9 - 5) x = ( 3)/( (9)5) Calculate the numerical value: x ≈ (1.0986)/(2.1972 - 1.6094) x ≈ (1.0986)/(0.5878) x ≈ 1.869 The value of x for science Vs library blocks is ( 3)/( (9)5) ≈ 1.869. b) For sports Vs agricultural plots: 7^4x+2 = 9^3x-1 Step 1: Take the natural logarithm (ln) of both sides of the equation. (7^4x+2) = (9^3x-1) Step 2: Apply the logarithm property (a^b) = b a to both sides. (4x+2) 7 = (3x-1) 9 Step 3: Distribute the logarithms on both sides. 4x 7 + 2 7 = 3x 9 - 9 Step 4: Gather terms containing x on one side and constant terms on the other. 4x 7 - 3x 9 = - 9 - 2 7 Step 5: Factor out x from the terms on the left side. x(4 7 - 3 9) = - ( 9 + 2 7) Step 6: Solve for x. x = (-( 9 + 2 7))/(4 7 - 3 9) Using logarithm properties, 2 7 = (7^2) = 49 and 4 7 = (7^4) = 2401 and 3 9 = (9^3) = 729. x = (-( 9 + 49))/( 2401 - 729) x = (- (9 × 49))/( (2401)729) x = (- (441))/( (2401)729) Calculate the numerical value: x ≈ (-(2.1972 + 2 × 1.9459))/(4 × 1.9459 - 3 × 2.1972) x ≈ (-(2.1972 + 3.8918))/(7.7836 - 6.5916) x ≈ (-6.089)/(1.192) x ≈ -5.108 The value of x for sports Vs agricultural plots is (- (441))/( (2401)729) ≈ -5.108. Last free one today — make it count tomorrow, or type /upgrade for unlimited.