Precalculus question

Question

Find the solution of the exponential equation in terms of logarithms, or correct to four decimal places.

T=___??

Answer 1

Hi Davie T.,

100(1.05)^2t = 500,000

1.05^2t = 5000...........................................[divide both sides by 100]

ln(1.05^2t) = ln(5000)................................[take the natural log of both sides]

2t*ln(1.05) = ln(5000)..............................[ln(a^b) = b*ln(a)]

2t = ln(5000)/ln(1.05)...............................[divide both sides by ln(1.05)]

t = ln(5000)/ln(1.05²) ≈ 87.2839..............[divide both sides by 2, b*ln(a) = ln(a^b)]

I hope this helps, Joe.