Use logarithms to solve the given equation. (Round the answer to four decimal places.) 4^2x = 37?

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

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

4 ² ˣ = 37

ln 4 ² ˣ = ln 37

2x ln 4 = ln 37

.......ln 37

x = ---------

.......2 ln 4

x ≈ 1.3024.................ANS

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