solve for t. 5=1.08^t+2
To solve for t, we can first subtract 2 from both sides of the equation:
5 - 2 = 1.08^t
This simplifies to:
3 = 1.08^t
Now, we need to isolate the variable t. To do so, we can take the logarithm base 1.08 of both sides of the equation:
log1.08(3) = log1.08(1.08^t)
Using the logarithmic property log_a(b^c) = c*log_a(b), we can rewrite the equation as:
log1.08(3) = t * log1.08(1.08)
Next, we need to calculate log1.08(3) and log1.08(1.08):
log1.08(3) ≈ 2.3096
log1.08(1.08) ≈ 0.0213
Now, we can substitute these values back into the equation:
2.3096 = t * 0.0213
To solve for t, we need to divide both sides of the equation by 0.0213:
t = 2.3096 / 0.0213
t ≈ 108.306
So, the value of t is approximately 108.306.