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.