la console
4^(2x) = 37
[4^(2)]^(x) = 37
16^(x) = 37
Ln[16^(x)] = Ln(37) → you know that: Ln(x^a) = a.Ln(x)
x.Ln(16) = Ln(37)
x = Ln(37) / Ln(16)
x ≈ 1.30236
Puzzling
Remember, exponents take precedence over multiplication, so as written your equation would be equivalent to:
16x = 37
x = 37/16
But obviously that doesn't require logarithms to solve. Be sure to always include the full exponent in parentheses.
4^(2x) = 37
Take the log of both sides:
log(4^(2x)) = log(37)
Use this rule --> log(a^b) = b log(a)
2x log(4) = log(37)
Divide both sides by 2 log(4)
x = log(37) / [2 log(4)]
x ≈ 1.3024
?
Assuming the parentheses were omitted and the equation should be:
4^(2x) = 37
16^(x) = 37
x = log(37)/log(16)
x ≈ 1.30236
?
Assuming it is 4^(2x) = 37
2xlog 4 = log 37
x = 1.3024
?
2x log 4 = log 37
x = log 37 / (2 log 4)
Now use your calculator and solve for x