How do I solve 15^x-8+5=62 And round 3 places past the decimal?

15^(x - 8) + 5 = 62

15^(x - 8) = 57

Ln[15^(x - 8)] = Ln(57)

(x - 8).Ln(15) = Ln(57)

x - 8 = Ln(57)/Ln(15)

x = 8 + [Ln(57)/Ln(15)]

x = [8.Ln(15) + Ln(57)]/Ln(15)

x ≈ 6.50702

x = 6.507

15^x - 8 + 5 = 62

15^x = 62 + 8 - 5

15^x = 65

x = (ln(65) + 2*i*pi*n) / ln(15), for any integer n

x =~ 1.541 + 2.320in, for any integer n

If x is a real number, then n = 0, so x = log[15](65) =~ 1.541

Looks at my answer to your other question which shows how to properly show what is in the exponent.

I have a feeling you mean:

15^(x - 8)  + 5 = 62

But without the proper parenthesis, there is no way to know.

15^x-8+5=62

15^x = 62+ 8 – 5 = 65

log base 15 (15^x) = log base 15 (65)

x = 1.541473

How about writing the question more clearly

15^x - 8 + 5 is the same as 15^x - 3. why write both -8 and 5

Or is it 15^(x-8)?

15^(x-8) = 57

log(57)/log(15) = 1.49

15^(x-8) = 15^(1.49)

x-8 = 1.49

x = 9.49

15^x - 8 + 5 = 62

15^x = 65

x = log(65)/log(15)

x ≈ 1.5415

15^x - 8 + 5 = 62

15^x = 62+8-5 = 65

xlog15 = log65

x = log65/log15 = 1.541