Question

Apply logarithm to evaluate T given 644 204=400 000 (1+10%)^T,by first simplify the equation.​

Answer 1

Answer:

T = 4.9988

Explanation:

Given the expression

$644 204=400 000 (1+10 \%)^T$

Since 10% = 0.1, the expression becomes;

$644 204=400 000 (1+0.1)^T\\644 204=400 000 (1.1)^T\\\frac{644204}{400000} =1.1^T\\1.61051=1.1^T$

Take the logarithm of both sides

$log1.61051=log1.1^T\\log1.61051=Tlog1.1\\Swap\\Tlog1.1=log1.61051\\T=\frac{log1.61051}{log1.1}\\T=\frac{0.2069}{0.04139} \\T=4.9988$

Hence the value of T is 4.9988