Sure! Let's solve the equation step-by-step.
We start with the equation:
[tex]\[ \log_4(3x + 7) = 3 \][/tex]
1. Convert the logarithmic equation to its exponential form:
The equation [tex]\( \log_b(y) = c \)[/tex] is equivalent to [tex]\( y = b^c \)[/tex].
Applying this rule:
[tex]\[ 3x + 7 = 4^3 \][/tex]
2. Calculate [tex]\( 4^3 \)[/tex]:
[tex]\[ 4^3 = 64 \][/tex]
So we have:
[tex]\[ 3x + 7 = 64 \][/tex]
3. Isolate the variable [tex]\( x \)[/tex]:
Subtract 7 from both sides to get:
[tex]\[ 3x = 64 - 7 \][/tex]
Simplify the right side:
[tex]\[ 3x = 57 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
Divide both sides by 3:
[tex]\[ x = \frac{57}{3} \][/tex]
Simplify the division:
[tex]\[ x = 19 \][/tex]
So, the solution is:
[tex]\[ x = 19 \][/tex]
