Step 1: Combine the terms on the left side using the index rule a^x × b^x = (a × b)^x. (2 × 3)^x = 8; 6^x = 8 Step 2: Take the logarithm of both sides. Using base 10 logarithm (lg) is convenient for calculation. log₁₀ (6^x) = log₁₀ 8; Step 3: Apply the power rule of logarithms, log_b (M^c) = c log_b M. x log₁₀ 6 = log₁₀ 8 Step 4: Solve for x. x = (log₁₀ 8)/(log₁₀ 6) Step 5: Calculate the numerical value and round to 3 significant figures. x ≈ 0.903089987/0.778151250 x ≈ 1.160559... Rounding to 3 significant figures: x = 1.16

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Solve for x: 6^x = 8

April 19, 2026Mathematics

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Answer

x = 1.16

Step-by-step solution

5 steps

Combine the terms on the left side using the index rule $a^x \times b^x = (a \times b)^x$ .
$(2 \times 3)^x = 8$ $6^x = 8$
Take the logarithm of both sides.
Using base 10 logarithm (lg) is convenient for calculation.
$\log_{10} (6^x) = \log_{10} 8$
Apply the power rule of logarithms, $\log_b (M^c) = c \log_b M$ .
$x \log_{10} 6 = \log_{10} 8$
Solve for $x$ .
$x = \frac{\log_{10} 8}{\log_{10} 6}$
Calculate the numerical value and round to 3 significant figures.
$x \approx \frac{0.903089987}{0.778151250}$ $x \approx 1.160559...$
Rounding to 3 significant figures:
$x = 1.16$

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Solve for x: 6^x = 8

Answer

Step-by-step solution

Combine the terms on the left side using the index rule ax×bx=(a×b)xa^x \times b^x = (a \times b)^xax×bx=(a×b)x.

Take the logarithm of both sides.

Apply the power rule of logarithms, log⁡b(Mc)=clog⁡bM\log_b (M^c) = c \log_b Mlogb​(Mc)=clogb​M.

Solve for xxx.

Calculate the numerical value and round to 3 significant figures.

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More Mathematics Questions

Combine the terms on the left side using the index rule $a^x \times b^x = (a \times b)^x$ .

Apply the power rule of logarithms, $\log_b (M^c) = c \log_b M$ .

Solve for $x$ .